Question
Answer
$$(x^3+5x^2+6x)(2x+2)-(x^2+2x+2)(3x^2+10x+6)=-x^4-4x^3-10x^2-20x-12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^3+5x^2+6x)(2x+2)-(x^2+2x+2)(3x^2+10x+6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^4+2x^3+10x^3+10x^2+12x^2+12x-(3x^4+16x^3+32x^2+32x+12) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^4+12x^3+22x^2+12x-(3x^4+16x^3+32x^2+32x+12) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^4+12x^3+22x^2+12x-3x^4-16x^3-32x^2-32x-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-x^4-4x^3-10x^2-20x-12\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^3+5x^2+6x}\right) $ by each term in $ \left( 2x+2\right) $. $$ \left( \color{blue}{x^3+5x^2+6x}\right) \cdot \left( 2x+2\right) = 2x^4+2x^3+10x^3+10x^2+12x^2+12x $$Multiply each term of $ \left( \color{blue}{x^2+2x+2}\right) $ by each term in $ \left( 3x^2+10x+6\right) $. $$ \left( \color{blue}{x^2+2x+2}\right) \cdot \left( 3x^2+10x+6\right) = 3x^4+10x^3+6x^2+6x^3+20x^2+12x+6x^2+20x+12 $$ |
| ② | Combine like terms: $$ 3x^4+ \color{blue}{10x^3} + \color{red}{6x^2} + \color{blue}{6x^3} + \color{green}{20x^2} + \color{orange}{12x} + \color{green}{6x^2} + \color{orange}{20x} +12 = \\ = 3x^4+ \color{blue}{16x^3} + \color{green}{32x^2} + \color{orange}{32x} +12 $$ |
| ③ | Combine like terms: $$ 2x^4+ \color{blue}{2x^3} + \color{blue}{10x^3} + \color{red}{10x^2} + \color{red}{12x^2} +12x = 2x^4+ \color{blue}{12x^3} + \color{red}{22x^2} +12x $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 3x^4+16x^3+32x^2+32x+12 \right) = -3x^4-16x^3-32x^2-32x-12 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{2x^4} + \color{red}{12x^3} + \color{green}{22x^2} + \color{orange}{12x} \color{blue}{-3x^4} \color{red}{-16x^3} \color{green}{-32x^2} \color{orange}{-32x} -12 = \\ = \color{blue}{-x^4} \color{red}{-4x^3} \color{green}{-10x^2} \color{orange}{-20x} -12 $$ |
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