Factor completely: 1-64r^(6) Answer:

Question Prompt: Question prompt: What is the factored form of the expression 1 - 64r^6?Recognize as Difference of Squares: Recognize the expression as a difference of squares. The expression 1 - 64r^6 can be written as 1^2 - (8r^3)^2, which is a difference of two squares.Apply Formula: Apply the difference of squares formula. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). Here, a = 1 and b = 8r^3.Factor Using Formula: Factor the expression using the formula. Substitute a and b into the formula to get (1 - 8r^3)(1 + 8r^3).Check Factored Expression: Check the factored expression. (1 - 8r^3)(1 + 8r^3) when multiplied out should give the original expression 1 - 64r^6. Let's check: (1 - 8r^3)(1 + 8r^3) = 1^2 - (8r^3)^2 = 1 - 64r^6, which matches the original expression.

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Q. Factor completely:

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1-64 r^{6}

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Answer:

Question Prompt: Question prompt: What is the factored form of the expression $1 - 64r^6$ ?
Recognize as Difference of Squares: Recognize the expression as a difference of squares. $\newline$ The expression $1 - 64r^6$ can be written as $1^2 - (8r^3)^2$ , which is a difference of two squares.
Apply Formula: Apply the difference of squares formula. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . Here, $a = 1$ and $b = 8r^3$ .
Factor Using Formula: Factor the expression using the formula. $\newline$ Substitute $a$ and $b$ into the formula to get $(1 - 8r^3)(1 + 8r^3)$ .
Check Factored Expression: Check the factored expression. $\newline$ $(1 - 8r^3)(1 + 8r^3)$ when multiplied out should give the original expression $1 - 64r^6$ . Let's check: $\newline$ $(1 - 8r^3)(1 + 8r^3) = 1^2 - (8r^3)^2 = 1 - 64r^6$ , which matches the original expression.