Question
Answer
$$(x+2)(x+2)(x+5)=x^3+9x^2+24x+20$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2)(x+2)(x+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+2x+2x+4)(x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+4x+4)(x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+5x^2+4x^2+20x+4x+20 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+9x^2+24x+20\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+2}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x+2}\right) \cdot \left( x+2\right) = x^2+2x+2x+4 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{2x} + \color{blue}{2x} +4 = x^2+ \color{blue}{4x} +4 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+4x+4}\right) $ by each term in $ \left( x+5\right) $. $$ \left( \color{blue}{x^2+4x+4}\right) \cdot \left( x+5\right) = x^3+5x^2+4x^2+20x+4x+20 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{5x^2} + \color{blue}{4x^2} + \color{red}{20x} + \color{red}{4x} +20 = x^3+ \color{blue}{9x^2} + \color{red}{24x} +20 $$ |
This page was created using
Simplify polynomials calculator