Question
Answer
$$(1-2x)^3\cdot(1-3x)=24x^4-44x^3+30x^2-9x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1-2x)^3\cdot(1-3x)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1-6x+12x^2-8x^3)\cdot(1-3x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}24x^4-44x^3+30x^2-9x+1\end{aligned} $$ | |
| ① | Find $ \left(1-2x\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = 1 $ and $ B = 2x $. $$ \left(1-2x\right)^3 = 1^3-3 \cdot 1^2 \cdot 2x + 3 \cdot 1 \cdot \left( 2x \right)^2-\left( 2x \right)^3 = 1-6x+12x^2-8x^3 $$ |
| ② | Multiply each term of $ \left( \color{blue}{1-6x+12x^2-8x^3}\right) $ by each term in $ \left( 1-3x\right) $. $$ \left( \color{blue}{1-6x+12x^2-8x^3}\right) \cdot \left( 1-3x\right) = 1-3x-6x+18x^2+12x^2-36x^3-8x^3+24x^4 $$ |
| ③ | Combine like terms: $$ 1 \color{blue}{-3x} \color{blue}{-6x} + \color{red}{18x^2} + \color{red}{12x^2} \color{green}{-36x^3} \color{green}{-8x^3} +24x^4 = 24x^4 \color{green}{-44x^3} + \color{red}{30x^2} \color{blue}{-9x} +1 $$ |
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