Question
Answer
$$(3x-1)(x-4)^2=3x^3-25x^2+56x-16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x-1)(x-4)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(3x-1)(x^2-8x+16) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3x^3-24x^2+48x-x^2+8x-16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3x^3-25x^2+56x-16\end{aligned} $$ | |
| ① | Find $ \left(x-4\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 4 }$. $$ \begin{aligned}\left(x-4\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 4 + \color{red}{4^2} = x^2-8x+16\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{3x-1}\right) $ by each term in $ \left( x^2-8x+16\right) $. $$ \left( \color{blue}{3x-1}\right) \cdot \left( x^2-8x+16\right) = 3x^3-24x^2+48x-x^2+8x-16 $$ |
| ③ | Combine like terms: $$ 3x^3 \color{blue}{-24x^2} + \color{red}{48x} \color{blue}{-x^2} + \color{red}{8x} -16 = 3x^3 \color{blue}{-25x^2} + \color{red}{56x} -16 $$ |
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