Question
Answer
$$(4x^2-16x+17)(x^2+2x+1)=4x^4-8x^3-11x^2+18x+17$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4x^2-16x+17)(x^2+2x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^4-8x^3-11x^2+18x+17\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{4x^2-16x+17}\right) $ by each term in $ \left( x^2+2x+1\right) $. $$ \left( \color{blue}{4x^2-16x+17}\right) \cdot \left( x^2+2x+1\right) = 4x^4+8x^3+4x^2-16x^3-32x^2-16x+17x^2+34x+17 $$ |
| ② | Combine like terms: $$ 4x^4+ \color{blue}{8x^3} + \color{red}{4x^2} \color{blue}{-16x^3} \color{green}{-32x^2} \color{orange}{-16x} + \color{green}{17x^2} + \color{orange}{34x} +17 = \\ = 4x^4 \color{blue}{-8x^3} \color{green}{-11x^2} + \color{orange}{18x} +17 $$ |
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