Question
Answer
$$(x-4)(x-4)(x-4)=x^3-12x^2+48x-64$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-4)(x-4)(x-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-4x-4x+16)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-8x+16)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-4x^2-8x^2+32x+16x-64 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-12x^2+48x-64\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-4}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x-4}\right) \cdot \left( x-4\right) = x^2-4x-4x+16 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-4x} \color{blue}{-4x} +16 = x^2 \color{blue}{-8x} +16 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-8x+16}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x^2-8x+16}\right) \cdot \left( x-4\right) = x^3-4x^2-8x^2+32x+16x-64 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-4x^2} \color{blue}{-8x^2} + \color{red}{32x} + \color{red}{16x} -64 = x^3 \color{blue}{-12x^2} + \color{red}{48x} -64 $$ |
This page was created using
Simplify polynomials calculator