Question
Answer
$$(7x^2-4x+7)(6x^2-x-3)=42x^4-31x^3+25x^2+5x-21$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(7x^2-4x+7)(6x^2-x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}42x^4-31x^3+25x^2+5x-21\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{7x^2-4x+7}\right) $ by each term in $ \left( 6x^2-x-3\right) $. $$ \left( \color{blue}{7x^2-4x+7}\right) \cdot \left( 6x^2-x-3\right) = 42x^4-7x^3-21x^2-24x^3+4x^2+12x+42x^2-7x-21 $$ |
| ② | Combine like terms: $$ 42x^4 \color{blue}{-7x^3} \color{red}{-21x^2} \color{blue}{-24x^3} + \color{green}{4x^2} + \color{orange}{12x} + \color{green}{42x^2} \color{orange}{-7x} -21 = \\ = 42x^4 \color{blue}{-31x^3} + \color{green}{25x^2} + \color{orange}{5x} -21 $$ |
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