Evaluate
\left(x-2\right)\left(3x^{3}+2x+4\right)
Expand
3x^{4}-6x^{3}+2x^{2}-8
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\left(3x^{2}-6x\right)\left(x^{2}+1\right)+\left(x-4\right)\left(2-x\right)
Use the distributive property to multiply 3x by x-2.
3x^{4}+3x^{2}-6x^{3}-6x+\left(x-4\right)\left(2-x\right)
Use the distributive property to multiply 3x^{2}-6x by x^{2}+1.
3x^{4}+3x^{2}-6x^{3}-6x+6x-x^{2}-8
Use the distributive property to multiply x-4 by 2-x and combine like terms.
3x^{4}+3x^{2}-6x^{3}-x^{2}-8
Combine -6x and 6x to get 0.
3x^{4}+2x^{2}-6x^{3}-8
Combine 3x^{2} and -x^{2} to get 2x^{2}.
\left(3x^{2}-6x\right)\left(x^{2}+1\right)+\left(x-4\right)\left(2-x\right)
Use the distributive property to multiply 3x by x-2.
3x^{4}+3x^{2}-6x^{3}-6x+\left(x-4\right)\left(2-x\right)
Use the distributive property to multiply 3x^{2}-6x by x^{2}+1.
3x^{4}+3x^{2}-6x^{3}-6x+6x-x^{2}-8
Use the distributive property to multiply x-4 by 2-x and combine like terms.
3x^{4}+3x^{2}-6x^{3}-x^{2}-8
Combine -6x and 6x to get 0.
3x^{4}+2x^{2}-6x^{3}-8
Combine 3x^{2} and -x^{2} to get 2x^{2}.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
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}