Question
Answer
$$3x(x-5)(x+2)(x+7)=3x^4+12x^3-93x^2-210x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3x(x-5)(x+2)(x+7)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(3x^2-15x)(x+2)(x+7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(3x^3+6x^2-15x^2-30x)(x+7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(3x^3-9x^2-30x)(x+7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3x^4+21x^3-9x^3-63x^2-30x^2-210x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}3x^4+12x^3-93x^2-210x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3x} $ by $ \left( x-5\right) $ $$ \color{blue}{3x} \cdot \left( x-5\right) = 3x^2-15x $$ |
| ② | Multiply each term of $ \left( \color{blue}{3x^2-15x}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{3x^2-15x}\right) \cdot \left( x+2\right) = 3x^3+6x^2-15x^2-30x $$ |
| ③ | Combine like terms: $$ 3x^3+ \color{blue}{6x^2} \color{blue}{-15x^2} -30x = 3x^3 \color{blue}{-9x^2} -30x $$ |
| ④ | Multiply each term of $ \left( \color{blue}{3x^3-9x^2-30x}\right) $ by each term in $ \left( x+7\right) $. $$ \left( \color{blue}{3x^3-9x^2-30x}\right) \cdot \left( x+7\right) = 3x^4+21x^3-9x^3-63x^2-30x^2-210x $$ |
| ⑤ | Combine like terms: $$ 3x^4+ \color{blue}{21x^3} \color{blue}{-9x^3} \color{red}{-63x^2} \color{red}{-30x^2} -210x = 3x^4+ \color{blue}{12x^3} \color{red}{-93x^2} -210x $$ |
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