Question
Answer
$$(x^2+3x+2)(2x+3)-(x^2-3x+2)(2x-3)=18x^2+12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+3x+2)(2x+3)-(x^2-3x+2)(2x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2x^3+3x^2+6x^2+9x+4x+6-(2x^3-3x^2-6x^2+9x+4x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^3+9x^2+13x+6-(2x^3-9x^2+13x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3+9x^2+13x+6-2x^3+9x^2-13x+6 \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{2x^3}+9x^2+ \cancel{13x}+6 -\cancel{2x^3}+9x^2 -\cancel{13x}+6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}18x^2+12\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2+3x+2}\right) $ by each term in $ \left( 2x+3\right) $. $$ \left( \color{blue}{x^2+3x+2}\right) \cdot \left( 2x+3\right) = 2x^3+3x^2+6x^2+9x+4x+6 $$Multiply each term of $ \left( \color{blue}{x^2-3x+2}\right) $ by each term in $ \left( 2x-3\right) $. $$ \left( \color{blue}{x^2-3x+2}\right) \cdot \left( 2x-3\right) = 2x^3-3x^2-6x^2+9x+4x-6 $$ |
| ② | Combine like terms: $$ 2x^3+ \color{blue}{3x^2} + \color{blue}{6x^2} + \color{red}{9x} + \color{red}{4x} +6 = 2x^3+ \color{blue}{9x^2} + \color{red}{13x} +6 $$Combine like terms: $$ 2x^3 \color{blue}{-3x^2} \color{blue}{-6x^2} + \color{red}{9x} + \color{red}{4x} -6 = 2x^3 \color{blue}{-9x^2} + \color{red}{13x} -6 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2x^3-9x^2+13x-6 \right) = -2x^3+9x^2-13x+6 $$ |
| ④ | Combine like terms: $$ \, \color{blue}{ \cancel{2x^3}} \,+ \color{green}{9x^2} + \, \color{orange}{ \cancel{13x}} \,+ \color{red}{6} \, \color{blue}{ -\cancel{2x^3}} \,+ \color{green}{9x^2} \, \color{orange}{ -\cancel{13x}} \,+ \color{red}{6} = \color{green}{18x^2} + \color{red}{12} $$ |
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