Question
Answer
$$2(x+3)(x-3)(x+4)(x-5)=2x^4-2x^3-58x^2+18x+360$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x+3)(x-3)(x+4)(x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x+6)(x-3)(x+4)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2-6x+6x-18)(x+4)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(2x^2-18)(x+4)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(2x^3+8x^2-18x-72)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}2x^4-2x^3-58x^2+18x+360\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( x+3\right) $ $$ \color{blue}{2} \cdot \left( x+3\right) = 2x+6 $$ |
| ② | Multiply each term of $ \left( \color{blue}{2x+6}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{2x+6}\right) \cdot \left( x-3\right) = 2x^2 -\cancel{6x}+ \cancel{6x}-18 $$ |
| ③ | Combine like terms: $$ 2x^2 \, \color{blue}{ -\cancel{6x}} \,+ \, \color{blue}{ \cancel{6x}} \,-18 = 2x^2-18 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{2x^2-18}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{2x^2-18}\right) \cdot \left( x+4\right) = 2x^3+8x^2-18x-72 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{2x^3+8x^2-18x-72}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{2x^3+8x^2-18x-72}\right) \cdot \left( x-5\right) = 2x^4-10x^3+8x^3-40x^2-18x^2+90x-72x+360 $$ |
| ⑥ | Combine like terms: $$ 2x^4 \color{blue}{-10x^3} + \color{blue}{8x^3} \color{red}{-40x^2} \color{red}{-18x^2} + \color{green}{90x} \color{green}{-72x} +360 = \\ = 2x^4 \color{blue}{-2x^3} \color{red}{-58x^2} + \color{green}{18x} +360 $$ |
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