Question
Answer
$$-(x+4)^2(x-1)(x+2)(2x-3)=-2x^5-15x^4-17x^3+66x^2+64x-96$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-(x+4)^2(x-1)(x+2)(2x-3)& \xlongequal{ }-(x^2+8x+16)(x-1)(x+2)(2x-3) \xlongequal{ } \\[1 em] & \xlongequal{ }-(x^3-x^2+8x^2-8x+16x-16)(x+2)(2x-3) \xlongequal{ } \\[1 em] & \xlongequal{ }-(x^3+7x^2+8x-16)(x+2)(2x-3) \xlongequal{ } \\[1 em] & \xlongequal{ }-(x^4+9x^3+22x^2-32)(2x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-(2x^5+15x^4+17x^3-66x^2-64x+96) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2x^5-15x^4-17x^3+66x^2+64x-96\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^4+9x^3+22x^2-32}\right) $ by each term in $ \left( 2x-3\right) $. $$ \left( \color{blue}{x^4+9x^3+22x^2-32}\right) \cdot \left( 2x-3\right) = 2x^5-3x^4+18x^4-27x^3+44x^3-66x^2-64x+96 $$ |
| ② | Combine like terms: $$ 2x^5 \color{blue}{-3x^4} + \color{blue}{18x^4} \color{red}{-27x^3} + \color{red}{44x^3} -66x^2-64x+96 = 2x^5+ \color{blue}{15x^4} + \color{red}{17x^3} -66x^2-64x+96 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left(2x^5+15x^4+17x^3-66x^2-64x+96 \right) = -2x^5-15x^4-17x^3+66x^2+64x-96 $$ |
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