Question
Answer
$$x^2(x-6)-(x-2)^3=-12x+8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x^2(x-6)-(x-2)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2(x-6)-(x^3-6x^2+12x-8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3-6x^2-(x^3-6x^2+12x-8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-6x^2-x^3+6x^2-12x+8 \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{x^3} -\cancel{6x^2} -\cancel{x^3}+ \cancel{6x^2}-12x+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-12x+8\end{aligned} $$ | |
| ① | Find $ \left(x-2\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = x $ and $ B = 2 $. $$ \left(x-2\right)^3 = x^3-3 \cdot x^2 \cdot 2 + 3 \cdot x \cdot 2^2-2^3 = x^3-6x^2+12x-8 $$ |
| ② | Multiply $ \color{blue}{x^2} $ by $ \left( x-6\right) $ $$ \color{blue}{x^2} \cdot \left( x-6\right) = x^3-6x^2 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( x^3-6x^2+12x-8 \right) = -x^3+6x^2-12x+8 $$ |
| ④ | Combine like terms: $$ \, \color{blue}{ \cancel{x^3}} \, \, \color{green}{ -\cancel{6x^2}} \, \, \color{blue}{ -\cancel{x^3}} \,+ \, \color{green}{ \cancel{6x^2}} \,-12x+8 = -12x+8 $$ |
This page was created using
Simplify polynomials calculator