Question
Answer
$$(x-4)(3x-1)^2=9x^3-42x^2+25x-4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-4)(3x-1)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x-4)(9x^2-6x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9x^3-6x^2+x-36x^2+24x-4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}9x^3-42x^2+25x-4\end{aligned} $$ | |
| ① | Find $ \left(3x-1\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 3x } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(3x-1\right)^2 = \color{blue}{\left( 3x \right)^2} -2 \cdot 3x \cdot 1 + \color{red}{1^2} = 9x^2-6x+1\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x-4}\right) $ by each term in $ \left( 9x^2-6x+1\right) $. $$ \left( \color{blue}{x-4}\right) \cdot \left( 9x^2-6x+1\right) = 9x^3-6x^2+x-36x^2+24x-4 $$ |
| ③ | Combine like terms: $$ 9x^3 \color{blue}{-6x^2} + \color{red}{x} \color{blue}{-36x^2} + \color{red}{24x} -4 = 9x^3 \color{blue}{-42x^2} + \color{red}{25x} -4 $$ |
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