Question
Answer
$$(3n-x)(45n^2-15nx+15n-5x-6)=135n^3-90n^2x+15nx^2+45n^2-30nx+5x^2-18n+6x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3n-x)(45n^2-15nx+15n-5x-6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}135n^3-90n^2x+15nx^2+45n^2-30nx+5x^2-18n+6x\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3n-x}\right) $ by each term in $ \left( 45n^2-15nx+15n-5x-6\right) $. $$ \left( \color{blue}{3n-x}\right) \cdot \left( 45n^2-15nx+15n-5x-6\right) = \\ = 135n^3-45n^2x+45n^2-15nx-18n-45n^2x+15nx^2-15nx+5x^2+6x $$ |
| ② | Combine like terms: $$ 135n^3 \color{blue}{-45n^2x} +45n^2 \color{red}{-15nx} -18n \color{blue}{-45n^2x} +15nx^2 \color{red}{-15nx} +5x^2+6x = \\ = 135n^3 \color{blue}{-90n^2x} +15nx^2+45n^2 \color{red}{-30nx} +5x^2-18n+6x $$ |
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