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