Question
Answer
$$2(3x-2)-4(x-1)(2x+5)(2x+5)=-16x^3-64x^2-14x+96$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(3x-2)-4(x-1)(2x+5)(2x+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6x-4-(4x-4)(2x+5)(2x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6x-4-(8x^2+20x-8x-20)(2x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6x-4-(8x^2+12x-20)(2x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}6x-4-(16x^3+40x^2+24x^2+60x-40x-100) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}6x-4-(16x^3+64x^2+20x-100) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}6x-4-16x^3-64x^2-20x+100 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}-16x^3-64x^2-14x+96\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( 3x-2\right) $ $$ \color{blue}{2} \cdot \left( 3x-2\right) = 6x-4 $$Multiply $ \color{blue}{4} $ by $ \left( x-1\right) $ $$ \color{blue}{4} \cdot \left( x-1\right) = 4x-4 $$ |
| ② | Multiply each term of $ \left( \color{blue}{4x-4}\right) $ by each term in $ \left( 2x+5\right) $. $$ \left( \color{blue}{4x-4}\right) \cdot \left( 2x+5\right) = 8x^2+20x-8x-20 $$ |
| ③ | Combine like terms: $$ 8x^2+ \color{blue}{20x} \color{blue}{-8x} -20 = 8x^2+ \color{blue}{12x} -20 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{8x^2+12x-20}\right) $ by each term in $ \left( 2x+5\right) $. $$ \left( \color{blue}{8x^2+12x-20}\right) \cdot \left( 2x+5\right) = 16x^3+40x^2+24x^2+60x-40x-100 $$ |
| ⑤ | Combine like terms: $$ 16x^3+ \color{blue}{40x^2} + \color{blue}{24x^2} + \color{red}{60x} \color{red}{-40x} -100 = 16x^3+ \color{blue}{64x^2} + \color{red}{20x} -100 $$ |
| ⑥ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 16x^3+64x^2+20x-100 \right) = -16x^3-64x^2-20x+100 $$ |
| ⑦ | Combine like terms: $$ \color{blue}{6x} \color{red}{-4} -16x^3-64x^2 \color{blue}{-20x} + \color{red}{100} = -16x^3-64x^2 \color{blue}{-14x} + \color{red}{96} $$ |
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