Question
Answer
$$(3x^2+x+6)(4x^2-7x-7)=12x^4-17x^3-4x^2-49x-42$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x^2+x+6)(4x^2-7x-7)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}12x^4-17x^3-4x^2-49x-42\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3x^2+x+6}\right) $ by each term in $ \left( 4x^2-7x-7\right) $. $$ \left( \color{blue}{3x^2+x+6}\right) \cdot \left( 4x^2-7x-7\right) = 12x^4-21x^3-21x^2+4x^3-7x^2-7x+24x^2-42x-42 $$ |
| ② | Combine like terms: $$ 12x^4 \color{blue}{-21x^3} \color{red}{-21x^2} + \color{blue}{4x^3} \color{green}{-7x^2} \color{orange}{-7x} + \color{green}{24x^2} \color{orange}{-42x} -42 = \\ = 12x^4 \color{blue}{-17x^3} \color{green}{-4x^2} \color{orange}{-49x} -42 $$ |
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