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

Apply Power to Terms: Apply the power to each term inside the parentheses. When raising a binomial to the power of 2, we square each term and also include the cross-product term, which is 2 times the product of the two terms. So, (a - b)^2 = a^2 - 2ab + b^2. In this case, a = 4x^5 and b = y^5. Therefore, (4x^5 - y^5)^2 = (4x^5)^2 - 2*(4x^5)*(y^5) + (y^5)^2.Calculate Each Term: Calculate each term separately. (4x^5)^2 = 16x^10 (since (4^2)*(x^5)^2 = 16x^10), -2*(4x^5)*(y^5) = -8x^5y^5 (since 2*4*x^5*y^5 = 8x^5y^5), (y^5)^2 = y^10 (since (y^5)^2 = y^10).Combine Results: Combine the results from Step 2. The fully simplified form of the expression is 16x^10 - 8x^5y^5 + y^10.

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Fully simplify.

(4x^(5)-y^(5))^(2)
Answer:

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

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Algebra 2

Find trigonometric ratios using reference angles

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Q. Fully simplify.

\newline

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

\newline

Answer:

Apply Power to Terms: Apply the power to each term inside the parentheses. $\newline$ When raising a binomial to the power of $2$ , we square each term and also include the cross-product term, which is $2$ times the product of the two terms. So, $(a - b)^2 = a^2 - 2ab + b^2$ . $\newline$ In this case, $a = 4x^5$ and $b = y^5$ . $\newline$ Therefore, $(4x^5 - y^5)^2 = (4x^5)^2 - 2\times(4x^5)\times(y^5) + (y^5)^2$ .
Calculate Each Term: Calculate each term separately. $\newline$ $(4x^5)^2 = 16x^{10}$ (since $(4^2)\cdot(x^5)^2 = 16x^{10}$ ), $\newline$ $-2\cdot(4x^5)\cdot(y^5) = -8x^5y^5$ (since $2\cdot4\cdot x^5\cdot y^5 = 8x^5y^5$ ), $\newline$ $(y^5)^2 = y^{10}$ (since $(y^5)^2 = y^{10}$ ).
Combine Results: Combine the results from Step $2$ . $\newline$ The fully simplified form of the expression is $16x^{10} - 8x^{5}y^{5} + y^{10}.$