Using long division, perform the operation below. (a^(6)-64b^(6))÷(a-2b)

Set Up Long Division: First, set up the long division by writing the dividend (a^6 - 64b^6) and the divisor (a - 2b).Divide First Terms: Divide the first term of the dividend, a^6, by the first term of the divisor, a, to get the first term of the quotient, a^5.Multiply and Subtract: Multiply the entire divisor (a - 2b) by the first term of the quotient (a^5) to get a^6 - 2a^5b.Divide New Dividend: Subtract the result (a^6 - 2a^5b) from the dividend (a^6 - 64b^6) to get the new dividend. Since a^6 cancels out, we are left with 2a^5b - 64b^6.Repeat Division Steps: Divide the first term of the new dividend, 2a^5b, by the first term of the divisor, a, to get the next term of the quotient, 2a^4b.Complete Division: Multiply the entire divisor (a - 2b) by the new term of the quotient (2a^4b) to get 2a^5b - 4a^4b^2.Subtract the result (2a^5b - 4a^4b^2) from the new dividend (2a^5b - 64b^6) to get the next new dividend. Since 2a^5b cancels out, we are left with 4a^4b^2 - 64b^6.Divide the first term of the next new dividend, 4a^4b^2, by the first term of the divisor, a, to get the next term of the quotient, 4a^3b^2.Multiply the entire divisor (a - 2b) by the new term of the quotient (4a^3b^2) to get 4a^4b^2 - 8a^3b^3.Subtract the result (4a^4b^2 - 8a^3b^3) from the next new dividend (4a^4b^2 - 64b^6) to get the next new dividend. Since 4a^4b^2 cancels out, we are left with 8a^3b^3 - 64b^6.Divide the first term of the next new dividend, 8a^3b^3, by the first term of the divisor, a, to get the next term of the quotient, 8a^2b^3.Multiply the entire divisor (a - 2b) by the new term of the quotient (8a^2b^3) to get 8a^3b^3 - 16a^2b^4.Subtract the result (8a^3b^3 - 16a^2b^4) from the next new dividend (8a^3b^3 - 64b^6) to get the next new dividend. Since 8a^3b^3 cancels out, we are left with 16a^2b^4 - 64b^6.Divide the first term of the next new dividend, 16a^2b^4, by the first term of the divisor, a, to get the next term of the quotient, 16ab^4.Multiply the entire divisor (a - 2b) by the new term of the quotient (16ab^4) to get 16a^2b^4 - 32ab^5.Subtract the result (16a^2b^4 - 32ab^5) from the next new dividend (16a^2b^4 - 64b^6) to get the next new dividend. Since 16a^2b^4 cancels out, we are left with 32ab^5 - 64b^6.Divide the first term of the next new dividend, 32ab^5, by the first term of the divisor, a, to get the next term of the quotient, 32b^5.Multiply the entire divisor (a - 2b) by the new term of the quotient (32b^5) to get 32ab^5 - 64b^6.Subtract the result (32ab^5 - 64b^6) from the next new dividend (32ab^5 - 64b^6) to get the next new dividend. Since both terms cancel out, we are left with 0, and the division is complete.

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Using long division, perform the operation below.

(a^(6)-64b^(6))÷(a-2b)

Using long division, perform the operation below. $\newline$ $(a^{6}-64b^{6})\div(a-2b)$

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Algebra 2

Divide polynomials using long division

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Q. Using long division, perform the operation below.

\newline

(a^{6}-64b^{6})\div(a-2b)

Set Up Long Division: First, set up the long division by writing the dividend $a^6 - 64b^6$ and the divisor $a - 2b$ .
Divide First Terms: Divide the first term of the dividend, $a^6$ , by the first term of the divisor, $a$ , to get the first term of the quotient, $a^5$ .
Multiply and Subtract: Multiply the entire divisor $(a - 2b)$ by the first term of the quotient $a^5$ to get $a^6 - 2a^5b$ .
Divide New Dividend: Subtract the result $a^6 - 2a^5b$ from the dividend $a^6 - 64b^6$ to get the new dividend. Since $a^6$ cancels out, we are left with $2a^5b - 64b^6$ .
Repeat Division Steps: Divide the first term of the new dividend, $2a^5b$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $2a^4b$ .
Complete Division: Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ to get $2a^5b - 4a^4b^2$ .
Complete Division: Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ to get $2a^5b - 4a^4b^2$ . Subtract the result $(2a^5b - 4a^4b^2)$ from the new dividend $(2a^5b - 64b^6)$ to get the next new dividend. Since $2a^5b$ cancels out, we are left with $4a^4b^2 - 64b^6$ .
Complete Division: Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ to get $2a^5b - 4a^4b^2$ . Subtract the result $(2a^5b - 4a^4b^2)$ from the new dividend $(2a^5b - 64b^6)$ to get the next new dividend. Since $2a^5b$ cancels out, we are left with $4a^4b^2 - 64b^6$ . Divide the first term of the next new dividend, $4a^4b^2$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $4a^3b^2$ .
Complete Division: Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ to get $2a^5b - 4a^4b^2$ . Subtract the result $(2a^5b - 4a^4b^2)$ from the new dividend $(2a^5b - 64b^6)$ to get the next new dividend. Since $2a^5b$ cancels out, we are left with $4a^4b^2 - 64b^6$ . Divide the first term of the next new dividend, $4a^4b^2$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $4a^3b^2$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ $1$ to get $(2a^4b)$ $2$ .
Complete Division: Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ to get $2a^5b - 4a^4b^2$ . Subtract the result $(2a^5b - 4a^4b^2)$ from the new dividend $(2a^5b - 64b^6)$ to get the next new dividend. Since $2a^5b$ cancels out, we are left with $4a^4b^2 - 64b^6$ . Divide the first term of the next new dividend, $4a^4b^2$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $4a^3b^2$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ $1$ to get $(2a^4b)$ $2$ . Subtract the result $(2a^4b)$ $3$ from the next new dividend $(2a^4b)$ $4$ to get the next new dividend. Since $4a^4b^2$ cancels out, we are left with $(2a^4b)$ $6$ .
Complete Division: Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ to get $2a^5b - 4a^4b^2$ . Subtract the result $(2a^5b - 4a^4b^2)$ from the new dividend $(2a^5b - 64b^6)$ to get the next new dividend. Since $2a^5b$ cancels out, we are left with $4a^4b^2 - 64b^6$ . Divide the first term of the next new dividend, $4a^4b^2$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $4a^3b^2$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ $1$ to get $(2a^4b)$ $2$ . Subtract the result $(2a^4b)$ $3$ from the next new dividend $(2a^4b)$ $4$ to get the next new dividend. Since $4a^4b^2$ cancels out, we are left with $(2a^4b)$ $6$ . Divide the first term of the next new dividend, $(2a^4b)$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $(2a^4b)$ $9$ .
Complete Division: Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ to get $2a^5b - 4a^4b^2$ . Subtract the result $(2a^5b - 4a^4b^2)$ from the new dividend $(2a^5b - 64b^6)$ to get the next new dividend. Since $2a^5b$ cancels out, we are left with $4a^4b^2 - 64b^6$ . Divide the first term of the next new dividend, $4a^4b^2$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $4a^3b^2$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ $1$ to get $(2a^4b)$ $2$ . Subtract the result $(2a^4b)$ $3$ from the next new dividend $(2a^4b)$ $4$ to get the next new dividend. Since $4a^4b^2$ cancels out, we are left with $(2a^4b)$ $6$ . Divide the first term of the next new dividend, $(2a^4b)$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $(2a^4b)$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $2a^5b - 4a^4b^2$ $1$ to get $2a^5b - 4a^4b^2$ $2$ .
Complete Division: Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ to get $2a^5b - 4a^4b^2$ . Subtract the result $(2a^5b - 4a^4b^2)$ from the new dividend $(2a^5b - 64b^6)$ to get the next new dividend. Since $2a^5b$ cancels out, we are left with $4a^4b^2 - 64b^6$ . Divide the first term of the next new dividend, $4a^4b^2$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $4a^3b^2$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ $1$ to get $(2a^4b)$ $2$ . Subtract the result $(2a^4b)$ $3$ from the next new dividend $(2a^4b)$ $4$ to get the next new dividend. Since $4a^4b^2$ cancels out, we are left with $(2a^4b)$ $6$ . Divide the first term of the next new dividend, $(2a^4b)$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $(2a^4b)$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $2a^5b - 4a^4b^2$ $1$ to get $2a^5b - 4a^4b^2$ $2$ . Subtract the result $2a^5b - 4a^4b^2$ $3$ from the next new dividend $2a^5b - 4a^4b^2$ $4$ to get the next new dividend. Since $(2a^4b)$ $7$ cancels out, we are left with $2a^5b - 4a^4b^2$ $6$ .
Complete Division: Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ to get $2a^5b - 4a^4b^2$ . Subtract the result $(2a^5b - 4a^4b^2)$ from the new dividend $(2a^5b - 64b^6)$ to get the next new dividend. Since $2a^5b$ cancels out, we are left with $4a^4b^2 - 64b^6$ . Divide the first term of the next new dividend, $4a^4b^2$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $4a^3b^2$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ $1$ to get $(2a^4b)$ $2$ . Subtract the result $(2a^4b)$ $3$ from the next new dividend $(2a^4b)$ $4$ to get the next new dividend. Since $4a^4b^2$ cancels out, we are left with $(2a^4b)$ $6$ . Divide the first term of the next new dividend, $(2a^4b)$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $(2a^4b)$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $2a^5b - 4a^4b^2$ $1$ to get $2a^5b - 4a^4b^2$ $2$ . Subtract the result $2a^5b - 4a^4b^2$ $3$ from the next new dividend $2a^5b - 4a^4b^2$ $4$ to get the next new dividend. Since $(2a^4b)$ $7$ cancels out, we are left with $2a^5b - 4a^4b^2$ $6$ . Divide the first term of the next new dividend, $2a^5b - 4a^4b^2$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $2a^5b - 4a^4b^2$ $9$ .
Complete Division: Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ to get $2a^5b - 4a^4b^2$ . Subtract the result $(2a^5b - 4a^4b^2)$ from the new dividend $(2a^5b - 64b^6)$ to get the next new dividend. Since $2a^5b$ cancels out, we are left with $4a^4b^2 - 64b^6$ . Divide the first term of the next new dividend, $4a^4b^2$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $4a^3b^2$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ $1$ to get $(2a^4b)$ $2$ . Subtract the result $(2a^4b)$ $3$ from the next new dividend $(2a^4b)$ $4$ to get the next new dividend. Since $4a^4b^2$ cancels out, we are left with $(2a^4b)$ $6$ . Divide the first term of the next new dividend, $(2a^4b)$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $(2a^4b)$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $2a^5b - 4a^4b^2$ $1$ to get $2a^5b - 4a^4b^2$ $2$ . Subtract the result $2a^5b - 4a^4b^2$ $3$ from the next new dividend $2a^5b - 4a^4b^2$ $4$ to get the next new dividend. Since $(2a^4b)$ $7$ cancels out, we are left with $2a^5b - 4a^4b^2$ $6$ . Divide the first term of the next new dividend, $2a^5b - 4a^4b^2$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $2a^5b - 4a^4b^2$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^5b - 4a^4b^2)$ $1$ to get $(2a^5b - 4a^4b^2)$ $2$ .
Complete Division: Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ to get $2a^5b - 4a^4b^2$ . Subtract the result $(2a^5b - 4a^4b^2)$ from the new dividend $(2a^5b - 64b^6)$ to get the next new dividend. Since $2a^5b$ cancels out, we are left with $4a^4b^2 - 64b^6$ . Divide the first term of the next new dividend, $4a^4b^2$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $4a^3b^2$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ $1$ to get $(2a^4b)$ $2$ . Subtract the result $(2a^4b)$ $3$ from the next new dividend $(2a^4b)$ $4$ to get the next new dividend. Since $4a^4b^2$ cancels out, we are left with $(2a^4b)$ $6$ . Divide the first term of the next new dividend, $(2a^4b)$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $(2a^4b)$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $2a^5b - 4a^4b^2$ $1$ to get $2a^5b - 4a^4b^2$ $2$ . Subtract the result $2a^5b - 4a^4b^2$ $3$ from the next new dividend $2a^5b - 4a^4b^2$ $4$ to get the next new dividend. Since $(2a^4b)$ $7$ cancels out, we are left with $2a^5b - 4a^4b^2$ $6$ . Divide the first term of the next new dividend, $2a^5b - 4a^4b^2$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $2a^5b - 4a^4b^2$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^5b - 4a^4b^2)$ $1$ to get $(2a^5b - 4a^4b^2)$ $2$ . Subtract the result $(2a^5b - 4a^4b^2)$ $3$ from the next new dividend $(2a^5b - 4a^4b^2)$ $4$ to get the next new dividend. Since $2a^5b - 4a^4b^2$ $7$ cancels out, we are left with $(2a^5b - 4a^4b^2)$ $6$ .
Complete Division: Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ to get $2a^5b - 4a^4b^2$ . Subtract the result $(2a^5b - 4a^4b^2)$ from the new dividend $(2a^5b - 64b^6)$ to get the next new dividend. Since $2a^5b$ cancels out, we are left with $4a^4b^2 - 64b^6$ . Divide the first term of the next new dividend, $4a^4b^2$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $4a^3b^2$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ $1$ to get $(2a^4b)$ $2$ . Subtract the result $(2a^4b)$ $3$ from the next new dividend $(2a^4b)$ $4$ to get the next new dividend. Since $4a^4b^2$ cancels out, we are left with $(2a^4b)$ $6$ . Divide the first term of the next new dividend, $(2a^4b)$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $(2a^4b)$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $2a^5b - 4a^4b^2$ $1$ to get $2a^5b - 4a^4b^2$ $2$ . Subtract the result $2a^5b - 4a^4b^2$ $3$ from the next new dividend $2a^5b - 4a^4b^2$ $4$ to get the next new dividend. Since $(2a^4b)$ $7$ cancels out, we are left with $2a^5b - 4a^4b^2$ $6$ . Divide the first term of the next new dividend, $2a^5b - 4a^4b^2$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $2a^5b - 4a^4b^2$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^5b - 4a^4b^2)$ $1$ to get $(2a^5b - 4a^4b^2)$ $2$ . Subtract the result $(2a^5b - 4a^4b^2)$ $3$ from the next new dividend $(2a^5b - 4a^4b^2)$ $4$ to get the next new dividend. Since $2a^5b - 4a^4b^2$ $7$ cancels out, we are left with $(2a^5b - 4a^4b^2)$ $6$ . Divide the first term of the next new dividend, $(2a^5b - 4a^4b^2)$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $(2a^5b - 4a^4b^2)$ $9$ .
Complete Division: Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ to get $2a^5b - 4a^4b^2$ . Subtract the result $(2a^5b - 4a^4b^2)$ from the new dividend $(2a^5b - 64b^6)$ to get the next new dividend. Since $2a^5b$ cancels out, we are left with $4a^4b^2 - 64b^6$ . Divide the first term of the next new dividend, $4a^4b^2$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $4a^3b^2$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ $1$ to get $(2a^4b)$ $2$ . Subtract the result $(2a^4b)$ $3$ from the next new dividend $(2a^4b)$ $4$ to get the next new dividend. Since $4a^4b^2$ cancels out, we are left with $(2a^4b)$ $6$ . Divide the first term of the next new dividend, $(2a^4b)$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $(2a^4b)$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $2a^5b - 4a^4b^2$ $1$ to get $2a^5b - 4a^4b^2$ $2$ . Subtract the result $2a^5b - 4a^4b^2$ $3$ from the next new dividend $2a^5b - 4a^4b^2$ $4$ to get the next new dividend. Since $(2a^4b)$ $7$ cancels out, we are left with $2a^5b - 4a^4b^2$ $6$ . Divide the first term of the next new dividend, $2a^5b - 4a^4b^2$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $2a^5b - 4a^4b^2$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^5b - 4a^4b^2)$ $1$ to get $(2a^5b - 4a^4b^2)$ $2$ . Subtract the result $(2a^5b - 4a^4b^2)$ $3$ from the next new dividend $(2a^5b - 4a^4b^2)$ $4$ to get the next new dividend. Since $2a^5b - 4a^4b^2$ $7$ cancels out, we are left with $(2a^5b - 4a^4b^2)$ $6$ . Divide the first term of the next new dividend, $(2a^5b - 4a^4b^2)$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $(2a^5b - 4a^4b^2)$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^5b - 64b^6)$ $1$ to get $(2a^5b - 4a^4b^2)$ $6$ .
Complete Division: Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ to get $2a^5b - 4a^4b^2$ . Subtract the result $(2a^5b - 4a^4b^2)$ from the new dividend $(2a^5b - 64b^6)$ to get the next new dividend. Since $2a^5b$ cancels out, we are left with $4a^4b^2 - 64b^6$ . Divide the first term of the next new dividend, $4a^4b^2$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $4a^3b^2$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^4b)$ $1$ to get $(2a^4b)$ $2$ . Subtract the result $(2a^4b)$ $3$ from the next new dividend $(2a^4b)$ $4$ to get the next new dividend. Since $4a^4b^2$ cancels out, we are left with $(2a^4b)$ $6$ . Divide the first term of the next new dividend, $(2a^4b)$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $(2a^4b)$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $2a^5b - 4a^4b^2$ $1$ to get $2a^5b - 4a^4b^2$ $2$ . Subtract the result $2a^5b - 4a^4b^2$ $3$ from the next new dividend $2a^5b - 4a^4b^2$ $4$ to get the next new dividend. Since $(2a^4b)$ $7$ cancels out, we are left with $2a^5b - 4a^4b^2$ $6$ . Divide the first term of the next new dividend, $2a^5b - 4a^4b^2$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $2a^5b - 4a^4b^2$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^5b - 4a^4b^2)$ $1$ to get $(2a^5b - 4a^4b^2)$ $2$ . Subtract the result $(2a^5b - 4a^4b^2)$ $3$ from the next new dividend $(2a^5b - 4a^4b^2)$ $4$ to get the next new dividend. Since $2a^5b - 4a^4b^2$ $7$ cancels out, we are left with $(2a^5b - 4a^4b^2)$ $6$ . Divide the first term of the next new dividend, $(2a^5b - 4a^4b^2)$ $7$ , by the first term of the divisor, $a$ , to get the next term of the quotient, $(2a^5b - 4a^4b^2)$ $9$ . Multiply the entire divisor $(a - 2b)$ by the new term of the quotient $(2a^5b - 64b^6)$ $1$ to get $(2a^5b - 4a^4b^2)$ $6$ . Subtract the result $(2a^5b - 64b^6)$ $3$ from the next new dividend $(2a^5b - 64b^6)$ $3$ to get the next new dividend. Since both terms cancel out, we are left with $(2a^5b - 64b^6)$ $5$ , and the division is complete.

Using long division, perform the operation below. $\newline$ $(a^{6}-64b^{6})\div(a-2b)$

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