Question
Answer
$$(2x-5)(2x-1)(2x-2)=8x^3-32x^2+34x-10$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x-5)(2x-1)(2x-2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4x^2-2x-10x+5)(2x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(4x^2-12x+5)(2x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}8x^3-8x^2-24x^2+24x+10x-10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}8x^3-32x^2+34x-10\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x-5}\right) $ by each term in $ \left( 2x-1\right) $. $$ \left( \color{blue}{2x-5}\right) \cdot \left( 2x-1\right) = 4x^2-2x-10x+5 $$ |
| ② | Combine like terms: $$ 4x^2 \color{blue}{-2x} \color{blue}{-10x} +5 = 4x^2 \color{blue}{-12x} +5 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{4x^2-12x+5}\right) $ by each term in $ \left( 2x-2\right) $. $$ \left( \color{blue}{4x^2-12x+5}\right) \cdot \left( 2x-2\right) = 8x^3-8x^2-24x^2+24x+10x-10 $$ |
| ④ | Combine like terms: $$ 8x^3 \color{blue}{-8x^2} \color{blue}{-24x^2} + \color{red}{24x} + \color{red}{10x} -10 = 8x^3 \color{blue}{-32x^2} + \color{red}{34x} -10 $$ |
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