Answer
$$x^2(x-5)^3=x^5-15x^4+75x^3-125x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x^2(x-5)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2(x^3-15x^2+75x-125) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^5-15x^4+75x^3-125x^2\end{aligned} $$ | |
| ① | Find $ \left(x-5\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = x $ and $ B = 5 $. $$ \left(x-5\right)^3 = x^3-3 \cdot x^2 \cdot 5 + 3 \cdot x \cdot 5^2-5^3 = x^3-15x^2+75x-125 $$ |
| ② | Multiply $ \color{blue}{x^2} $ by $ \left( x^3-15x^2+75x-125\right) $ $$ \color{blue}{x^2} \cdot \left( x^3-15x^2+75x-125\right) = x^5-15x^4+75x^3-125x^2 $$ |
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