Question
Answer
$$(x+4)(2x+2)(x+3)-3x(x+4)=2x^3+13x^2+26x+24$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+4)(2x+2)(x+3)-3x(x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x^2+2x+8x+8)(x+3)-(3x^2+12x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2+10x+8)(x+3)-(3x^2+12x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3+6x^2+10x^2+30x+8x+24-(3x^2+12x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^3+16x^2+38x+24-(3x^2+12x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}2x^3+16x^2+38x+24-3x^2-12x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}2x^3+13x^2+26x+24\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+4}\right) $ by each term in $ \left( 2x+2\right) $. $$ \left( \color{blue}{x+4}\right) \cdot \left( 2x+2\right) = 2x^2+2x+8x+8 $$Multiply $ \color{blue}{3x} $ by $ \left( x+4\right) $ $$ \color{blue}{3x} \cdot \left( x+4\right) = 3x^2+12x $$ |
| ② | Combine like terms: $$ 2x^2+ \color{blue}{2x} + \color{blue}{8x} +8 = 2x^2+ \color{blue}{10x} +8 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x^2+10x+8}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{2x^2+10x+8}\right) \cdot \left( x+3\right) = 2x^3+6x^2+10x^2+30x+8x+24 $$ |
| ④ | Combine like terms: $$ 2x^3+ \color{blue}{6x^2} + \color{blue}{10x^2} + \color{red}{30x} + \color{red}{8x} +24 = 2x^3+ \color{blue}{16x^2} + \color{red}{38x} +24 $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 3x^2+12x \right) = -3x^2-12x $$ |
| ⑥ | Combine like terms: $$ 2x^3+ \color{blue}{16x^2} + \color{red}{38x} +24 \color{blue}{-3x^2} \color{red}{-12x} = 2x^3+ \color{blue}{13x^2} + \color{red}{26x} +24 $$ |
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