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

Recognize Structure: Recognize the structure of the expression. The given expression is a binomial raised to the second power. This can be expanded using the formula (a - b)^2 = a^2 - 2ab + b^2, where a = 2x^5 and b = y^5.Apply Formula: Apply the binomial square formula. Using the formula from Step 1, we expand (2x^5 - y^5)^2 to get (2x^5)^2 - 2*(2x^5)*(y^5) + (y^5)^2.Calculate Terms: Calculate each term separately. First term: (2x^5)^2 = 4x^10 (since (2^2)*(x^5)^2 = 4x^10) Second term: 2*(2x^5)*(y^5) = 4x^5y^5 (since 2*2 = 4 and we just multiply the x^5 and y^5 terms) Third term: (y^5)^2 = y^10 (since (y^5)^2 = y^10)Combine Simplified Expression: Combine the terms to get the final simplified expression. The fully simplified form of the expression is 4x^10 - 4x^5y^5 + y^10.

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Fully simplify.

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

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

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Q. Fully simplify.

\newline

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

\newline

Answer:

Recognize Structure: Recognize the structure of the expression. $\newline$ The given expression is a binomial raised to the second power. This can be expanded using the formula $(a - b)^2 = a^2 - 2ab + b^2$ , where $a = 2x^5$ and $b = y^5$ .
Apply Formula: Apply the binomial square formula. $\newline$ Using the formula from Step $1$ , we expand $(2x^5 - y^5)^2$ to get $(2x^5)^2 - 2\cdot(2x^5)\cdot(y^5) + (y^5)^2$ .
Calculate Terms: Calculate each term separately. $\newline$ First term: $2x^5$ ^ $2$ = $4$ x^{ $10$ } $since \$2^2$ * $x^5$ ^ $2$ = $4$ x^{ $10$ }\) $\newline$ Second term: $2*(2x^5)*(y^5) = 4x^5y^5 \$since \$2*2 = 4$ and we just multiply the $x^5$ and $y^5$ terms)\) $\newline$ Third term: $y^5$ ^ $2$ = y^{ $10$ } since $y^5^ $2$ = y^{ $10$ }$
Combine Simplified Expression: Combine the terms to get the final simplified expression. $\newline$ The fully simplified form of the expression is $4x^{10} - 4x^{5}y^{5} + y^{10}.$