Question
Answer
$$(x^2+2hx+h^2)(x-1)=h^2x+2hx^2+x^3-h^2-2hx-x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+2hx+h^2)(x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^3-x^2+2hx^2-2hx+h^2x-h^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}h^2x+2hx^2+x^3-h^2-2hx-x^2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2+2hx+h^2}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{x^2+2hx+h^2}\right) \cdot \left( x-1\right) = x^3-x^2+2hx^2-2hx+h^2x-h^2 $$ |
| ② | Combine like terms: $$ h^2x+2hx^2+x^3-h^2-2hx-x^2 = h^2x+2hx^2+x^3-h^2-2hx-x^2 $$ |
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