Question
Answer
$$4(2x-7)(3x+2)-8(x-1)(3x-1)=-36x-64$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4(2x-7)(3x+2)-8(x-1)(3x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(8x-28)(3x+2)-(8x-8)(3x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}24x^2+16x-84x-56-(24x^2-8x-24x+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}24x^2-68x-56-(24x^2-32x+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}24x^2-68x-56-24x^2+32x-8 \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{24x^2}-68x-56 -\cancel{24x^2}+32x-8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-36x-64\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{4} $ by $ \left( 2x-7\right) $ $$ \color{blue}{4} \cdot \left( 2x-7\right) = 8x-28 $$Multiply $ \color{blue}{8} $ by $ \left( x-1\right) $ $$ \color{blue}{8} \cdot \left( x-1\right) = 8x-8 $$ |
| ② | Multiply each term of $ \left( \color{blue}{8x-28}\right) $ by each term in $ \left( 3x+2\right) $. $$ \left( \color{blue}{8x-28}\right) \cdot \left( 3x+2\right) = 24x^2+16x-84x-56 $$Multiply each term of $ \left( \color{blue}{8x-8}\right) $ by each term in $ \left( 3x-1\right) $. $$ \left( \color{blue}{8x-8}\right) \cdot \left( 3x-1\right) = 24x^2-8x-24x+8 $$ |
| ③ | Combine like terms: $$ 24x^2+ \color{blue}{16x} \color{blue}{-84x} -56 = 24x^2 \color{blue}{-68x} -56 $$Combine like terms: $$ 24x^2 \color{blue}{-8x} \color{blue}{-24x} +8 = 24x^2 \color{blue}{-32x} +8 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 24x^2-32x+8 \right) = -24x^2+32x-8 $$ |
| ⑤ | Combine like terms: $$ \, \color{blue}{ \cancel{24x^2}} \, \color{green}{-68x} \color{orange}{-56} \, \color{blue}{ -\cancel{24x^2}} \,+ \color{green}{32x} \color{orange}{-8} = \color{green}{-36x} \color{orange}{-64} $$ |
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