Question
Answer
$$16(x-2)^2(x-1)=16x^3-80x^2+128x-64$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}16(x-2)^2(x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}16(x^2-4x+4)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(16x^2-64x+64)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}16x^3-16x^2-64x^2+64x+64x-64 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}16x^3-80x^2+128x-64\end{aligned} $$ | |
| ① | Find $ \left(x-2\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(x-2\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 2 + \color{red}{2^2} = x^2-4x+4\end{aligned} $$ |
| ② | Multiply $ \color{blue}{16} $ by $ \left( x^2-4x+4\right) $ $$ \color{blue}{16} \cdot \left( x^2-4x+4\right) = 16x^2-64x+64 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{16x^2-64x+64}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{16x^2-64x+64}\right) \cdot \left( x-1\right) = 16x^3-16x^2-64x^2+64x+64x-64 $$ |
| ④ | Combine like terms: $$ 16x^3 \color{blue}{-16x^2} \color{blue}{-64x^2} + \color{red}{64x} + \color{red}{64x} -64 = 16x^3 \color{blue}{-80x^2} + \color{red}{128x} -64 $$ |
This page was created using
Simplify polynomials calculator