Fully simplify. (4x^(5)+y^(3))^(2) Answer:

Apply binomial expansion: Apply the binomial expansion to the expression (4x^(5)+y^(3))^(2). When we square a binomial, we use the formula (a+b)^2 = a^2 + 2ab + b^2. Here, a = 4x^5 and b = y^3.Calculate first term square: Calculate the square of the first term (4x^5)^2. (4x^5)^2 = 16x^(5*2) = 16x^10.Calculate product of terms: Calculate the product of the two terms multiplied by 2, which is 2*(4x^5)*(y^3). 2*(4x^5)*(y^3) = 8x^5*y^3.Calculate second term square: Calculate the square of the second term (y^3)^2. (y^3)^2 = y^(3*2) = y^6.Combine results for final form: Combine the results from steps 2, 3, and 4 to get the final expanded form. (4x^(5)+y^(3))^(2) = (4x^5)^2 + 2*(4x^5)*(y^3) + (y^3)^2 = 16x^10 + 8x^5*y^3 + y^6.

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Fully simplify.

(4x^(5)+y^(3))^(2)
Answer:

Fully simplify. $\newline$ $\left(4 x^{5}+y^{3}\right)^{2}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Fully simplify.

\newline

\left(4 x^{5}+y^{3}\right)^{2}

\newline

Answer:

Apply binomial expansion: Apply the binomial expansion to the expression $(4x^{5}+y^{3})^{2}$ . When we square a binomial, we use the formula $(a+b)^{2} = a^{2} + 2ab + b^{2}$ . Here, $a = 4x^{5}$ and $b = y^{3}$ .
Calculate first term square: Calculate the square of the first term $(4x^5)^2$ . $(4x^5)^2 = 16x^{(5*2)} = 16x^{10}$ .
Calculate product of terms: Calculate the product of the two terms multiplied by $2$ , which is $2 \times (4x^5) \times (y^3)$ . $\newline$ $2 \times (4x^5) \times (y^3) = 8x^5y^3$ .
Calculate second term square: Calculate the square of the second term $(y^3)^2$ . $(y^3)^2 = y^{(3*2)} = y^6$ .
Combine results for final form: Combine the results from steps $2$ , $3$ , and $4$ to get the final expanded form. $\newline$ (4x^{5}+y^{3})^{2} = (4x^5)^2 + 2\cdot(4x^5)\cdot(y^3) + (y^3)^2$\newline= 16x^{10} + 8x^5\cdot y^3 + y^6$.