Question
Answer
$$(2x^2+2x-6)(4x^2-7x-1)=8x^4-6x^3-40x^2+40x+6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x^2+2x-6)(4x^2-7x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8x^4-6x^3-40x^2+40x+6\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x^2+2x-6}\right) $ by each term in $ \left( 4x^2-7x-1\right) $. $$ \left( \color{blue}{2x^2+2x-6}\right) \cdot \left( 4x^2-7x-1\right) = 8x^4-14x^3-2x^2+8x^3-14x^2-2x-24x^2+42x+6 $$ |
| ② | Combine like terms: $$ 8x^4 \color{blue}{-14x^3} \color{red}{-2x^2} + \color{blue}{8x^3} \color{green}{-14x^2} \color{orange}{-2x} \color{green}{-24x^2} + \color{orange}{42x} +6 = \\ = 8x^4 \color{blue}{-6x^3} \color{green}{-40x^2} + \color{orange}{40x} +6 $$ |
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