Answer
$$(5x^2-y^5)^2=y^{10}-10x^2y^5+25x^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5x^2-y^5)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}25x^4-10x^2y^5+y^{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}y^{10}-10x^2y^5+25x^4\end{aligned} $$ | |
| ① | Find $ \left(5x^2-y^5\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 5x^2 } $ and $ B = \color{red}{ y^5 }$. $$ \begin{aligned}\left(5x^2-y^5\right)^2 = \color{blue}{\left( 5x^2 \right)^2} -2 \cdot 5x^2 \cdot y^5 + \color{red}{\left( y^5 \right)^2} = 25x^4-10x^2y^5+y^{10}\end{aligned} $$ |
| ② | Combine like terms: $$ y^{10}-10x^2y^5+25x^4 = y^{10}-10x^2y^5+25x^4 $$ |
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