Question
Answer
$$(x+2)^2(x-4)(x+9)=x^4+9x^3-12x^2-124x-144$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2)^2(x-4)(x+9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+4x+4)(x-4)(x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^3-4x^2+4x^2-16x+4x-16)(x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3-12x-16)(x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^4+9x^3-12x^2-108x-16x-144 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}x^4+9x^3-12x^2-124x-144\end{aligned} $$ | |
| ① | Find $ \left(x+2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(x+2\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 2 + \color{red}{2^2} = x^2+4x+4\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2+4x+4}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x^2+4x+4}\right) \cdot \left( x-4\right) = x^3 -\cancel{4x^2}+ \cancel{4x^2}-16x+4x-16 $$ |
| ③ | Combine like terms: $$ x^3 \, \color{blue}{ -\cancel{4x^2}} \,+ \, \color{blue}{ \cancel{4x^2}} \, \color{green}{-16x} + \color{green}{4x} -16 = x^3 \color{green}{-12x} -16 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{x^3-12x-16}\right) $ by each term in $ \left( x+9\right) $. $$ \left( \color{blue}{x^3-12x-16}\right) \cdot \left( x+9\right) = x^4+9x^3-12x^2-108x-16x-144 $$ |
| ⑤ | Combine like terms: $$ x^4+9x^3-12x^2 \color{blue}{-108x} \color{blue}{-16x} -144 = x^4+9x^3-12x^2 \color{blue}{-124x} -144 $$ |
This page was created using
Simplify polynomials calculator