Evaluate
-6x\left(x-2\right)
Expand
12x-6x^{2}
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x^{3}-6x^{2}+12x-8-\left(x-2\right)\left(x^{2}+2x+4\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-2\right)^{3}.
x^{3}-6x^{2}+12x-8-\left(x^{3}-8\right)
Use the distributive property to multiply x-2 by x^{2}+2x+4 and combine like terms.
x^{3}-6x^{2}+12x-8-x^{3}+8
To find the opposite of x^{3}-8, find the opposite of each term.
-6x^{2}+12x-8+8
Combine x^{3} and -x^{3} to get 0.
-6x^{2}+12x
Add -8 and 8 to get 0.
x^{3}-6x^{2}+12x-8-\left(x-2\right)\left(x^{2}+2x+4\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-2\right)^{3}.
x^{3}-6x^{2}+12x-8-\left(x^{3}-8\right)
Use the distributive property to multiply x-2 by x^{2}+2x+4 and combine like terms.
x^{3}-6x^{2}+12x-8-x^{3}+8
To find the opposite of x^{3}-8, find the opposite of each term.
-6x^{2}+12x-8+8
Combine x^{3} and -x^{3} to get 0.
-6x^{2}+12x
Add -8 and 8 to get 0.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}