Question
Answer
$$(x^2+2x+1)(x^2+4x+4)=x^4+6x^3+13x^2+12x+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+2x+1)(x^2+4x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^4+6x^3+13x^2+12x+4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2+2x+1}\right) $ by each term in $ \left( x^2+4x+4\right) $. $$ \left( \color{blue}{x^2+2x+1}\right) \cdot \left( x^2+4x+4\right) = x^4+4x^3+4x^2+2x^3+8x^2+8x+x^2+4x+4 $$ |
| ② | Combine like terms: $$ x^4+ \color{blue}{4x^3} + \color{red}{4x^2} + \color{blue}{2x^3} + \color{green}{8x^2} + \color{orange}{8x} + \color{green}{x^2} + \color{orange}{4x} +4 = \\ = x^4+ \color{blue}{6x^3} + \color{green}{13x^2} + \color{orange}{12x} +4 $$ |
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