Question
Answer
$$x^2(x-2)(5x+3)=5x^4-7x^3-6x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x^2(x-2)(5x+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^3-2x^2)(5x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5x^4+3x^3-10x^3-6x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5x^4-7x^3-6x^2\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{x^2} $ by $ \left( x-2\right) $ $$ \color{blue}{x^2} \cdot \left( x-2\right) = x^3-2x^2 $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^3-2x^2}\right) $ by each term in $ \left( 5x+3\right) $. $$ \left( \color{blue}{x^3-2x^2}\right) \cdot \left( 5x+3\right) = 5x^4+3x^3-10x^3-6x^2 $$ |
| ③ | Combine like terms: $$ 5x^4+ \color{blue}{3x^3} \color{blue}{-10x^3} -6x^2 = 5x^4 \color{blue}{-7x^3} -6x^2 $$ |
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