Question
Answer
$$(5x^2+4x-2)(7x^2-8x-3)=35x^4-12x^3-61x^2+4x+6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5x^2+4x-2)(7x^2-8x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}35x^4-12x^3-61x^2+4x+6\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5x^2+4x-2}\right) $ by each term in $ \left( 7x^2-8x-3\right) $. $$ \left( \color{blue}{5x^2+4x-2}\right) \cdot \left( 7x^2-8x-3\right) = 35x^4-40x^3-15x^2+28x^3-32x^2-12x-14x^2+16x+6 $$ |
| ② | Combine like terms: $$ 35x^4 \color{blue}{-40x^3} \color{red}{-15x^2} + \color{blue}{28x^3} \color{green}{-32x^2} \color{orange}{-12x} \color{green}{-14x^2} + \color{orange}{16x} +6 = \\ = 35x^4 \color{blue}{-12x^3} \color{green}{-61x^2} + \color{orange}{4x} +6 $$ |
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