Question
Answer
$$(x+3)(x-4)^3=x^4-9x^3+12x^2+80x-192$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+3)(x-4)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x+3)(x^3-12x^2+48x-64) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^4-9x^3+12x^2+80x-192\end{aligned} $$ | |
| ① | Find $ \left(x-4\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = x $ and $ B = 4 $. $$ \left(x-4\right)^3 = x^3-3 \cdot x^2 \cdot 4 + 3 \cdot x \cdot 4^2-4^3 = x^3-12x^2+48x-64 $$ |
| ② | Multiply each term of $ \left( \color{blue}{x+3}\right) $ by each term in $ \left( x^3-12x^2+48x-64\right) $. $$ \left( \color{blue}{x+3}\right) \cdot \left( x^3-12x^2+48x-64\right) = x^4-12x^3+48x^2-64x+3x^3-36x^2+144x-192 $$ |
| ③ | Combine like terms: $$ x^4 \color{blue}{-12x^3} + \color{red}{48x^2} \color{green}{-64x} + \color{blue}{3x^3} \color{red}{-36x^2} + \color{green}{144x} -192 = x^4 \color{blue}{-9x^3} + \color{red}{12x^2} + \color{green}{80x} -192 $$ |
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