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