Answer
$$(x-7)(2x+5)(x-3)=2x^3-15x^2-8x+105$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-7)(2x+5)(x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x^2+5x-14x-35)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2-9x-35)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3-6x^2-9x^2+27x-35x+105 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^3-15x^2-8x+105\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-7}\right) $ by each term in $ \left( 2x+5\right) $. $$ \left( \color{blue}{x-7}\right) \cdot \left( 2x+5\right) = 2x^2+5x-14x-35 $$ |
| ② | Combine like terms: $$ 2x^2+ \color{blue}{5x} \color{blue}{-14x} -35 = 2x^2 \color{blue}{-9x} -35 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x^2-9x-35}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{2x^2-9x-35}\right) \cdot \left( x-3\right) = 2x^3-6x^2-9x^2+27x-35x+105 $$ |
| ④ | Combine like terms: $$ 2x^3 \color{blue}{-6x^2} \color{blue}{-9x^2} + \color{red}{27x} \color{red}{-35x} +105 = 2x^3 \color{blue}{-15x^2} \color{red}{-8x} +105 $$ |
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