Question
Answer
$$x(x+2)(x^2+4x+5)=x^4+6x^3+13x^2+10x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x(x+2)(x^2+4x+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+2x)(x^2+4x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^4+4x^3+5x^2+2x^3+8x^2+10x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^4+6x^3+13x^2+10x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{x} $ by $ \left( x+2\right) $ $$ \color{blue}{x} \cdot \left( x+2\right) = x^2+2x $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2+2x}\right) $ by each term in $ \left( x^2+4x+5\right) $. $$ \left( \color{blue}{x^2+2x}\right) \cdot \left( x^2+4x+5\right) = x^4+4x^3+5x^2+2x^3+8x^2+10x $$ |
| ③ | Combine like terms: $$ x^4+ \color{blue}{4x^3} + \color{red}{5x^2} + \color{blue}{2x^3} + \color{red}{8x^2} +10x = x^4+ \color{blue}{6x^3} + \color{red}{13x^2} +10x $$ |
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