Question
Answer
$$(x-4)^2+(3x+5)(x-4)=4x^2-15x-4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-4)^2+(3x+5)(x-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2-8x+16+(3x+5)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2-8x+16+3x^2-12x+5x-20 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^2-8x+16+3x^2-7x-20 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4x^2-15x-4\end{aligned} $$ | |
| 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+5}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{3x+5}\right) \cdot \left( x-4\right) = 3x^2-12x+5x-20 $$ |
| ③ | Combine like terms: $$ 3x^2 \color{blue}{-12x} + \color{blue}{5x} -20 = 3x^2 \color{blue}{-7x} -20 $$ |
| ④ | Combine like terms: $$ \color{blue}{x^2} \color{red}{-8x} + \color{green}{16} + \color{blue}{3x^2} \color{red}{-7x} \color{green}{-20} = \color{blue}{4x^2} \color{red}{-15x} \color{green}{-4} $$ |
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