Question
Answer
$$(x-6)(x-7)(x-3)=x^3-16x^2+81x-126$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-6)(x-7)(x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-7x-6x+42)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-13x+42)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-3x^2-13x^2+39x+42x-126 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-16x^2+81x-126\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-6}\right) $ by each term in $ \left( x-7\right) $. $$ \left( \color{blue}{x-6}\right) \cdot \left( x-7\right) = x^2-7x-6x+42 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-7x} \color{blue}{-6x} +42 = x^2 \color{blue}{-13x} +42 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-13x+42}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{x^2-13x+42}\right) \cdot \left( x-3\right) = x^3-3x^2-13x^2+39x+42x-126 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-3x^2} \color{blue}{-13x^2} + \color{red}{39x} + \color{red}{42x} -126 = x^3 \color{blue}{-16x^2} + \color{red}{81x} -126 $$ |
This page was created using
Simplify polynomials calculator