Question
Answer
$$(4x-1)(x+2)^2(x-5)=4x^4-5x^3-63x^2-64x+20$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4x-1)(x+2)^2(x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4x-1)(x^2+4x+4)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(4x^3+16x^2+16x-x^2-4x-4)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(4x^3+15x^2+12x-4)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}4x^4-5x^3-63x^2-64x+20\end{aligned} $$ | |
| ① | Find $ \left(x+2\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}{ 2 }$. $$ \begin{aligned}\left(x+2\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 2 + \color{red}{2^2} = x^2+4x+4\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{4x-1}\right) $ by each term in $ \left( x^2+4x+4\right) $. $$ \left( \color{blue}{4x-1}\right) \cdot \left( x^2+4x+4\right) = 4x^3+16x^2+16x-x^2-4x-4 $$ |
| ③ | Combine like terms: $$ 4x^3+ \color{blue}{16x^2} + \color{red}{16x} \color{blue}{-x^2} \color{red}{-4x} -4 = 4x^3+ \color{blue}{15x^2} + \color{red}{12x} -4 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{4x^3+15x^2+12x-4}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{4x^3+15x^2+12x-4}\right) \cdot \left( x-5\right) = 4x^4-20x^3+15x^3-75x^2+12x^2-60x-4x+20 $$ |
| ⑤ | Combine like terms: $$ 4x^4 \color{blue}{-20x^3} + \color{blue}{15x^3} \color{red}{-75x^2} + \color{red}{12x^2} \color{green}{-60x} \color{green}{-4x} +20 = 4x^4 \color{blue}{-5x^3} \color{red}{-63x^2} \color{green}{-64x} +20 $$ |
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