Answer
$$(4x-1)(x^2-7x+1)=4x^3-29x^2+11x-1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4x-1)(x^2-7x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4x^3-28x^2+4x-x^2+7x-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^3-29x^2+11x-1\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{4x-1}\right) $ by each term in $ \left( x^2-7x+1\right) $. $$ \left( \color{blue}{4x-1}\right) \cdot \left( x^2-7x+1\right) = 4x^3-28x^2+4x-x^2+7x-1 $$ |
| ② | Combine like terms: $$ 4x^3 \color{blue}{-28x^2} + \color{red}{4x} \color{blue}{-x^2} + \color{red}{7x} -1 = 4x^3 \color{blue}{-29x^2} + \color{red}{11x} -1 $$ |
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