Evaluate
2\left(\left(2-x\right)^{3}-4x^{2}\right)
Expand
16-24x+4x^{2}-2x^{3}
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2\left(2-x\right)^{3}-2x^{2}\times 4
Multiply x and x to get x^{2}.
2\left(8-12x+6x^{2}-x^{3}\right)-2x^{2}\times 4
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2-x\right)^{3}.
16-24x+12x^{2}-2x^{3}-2x^{2}\times 4
Use the distributive property to multiply 2 by 8-12x+6x^{2}-x^{3}.
16-24x+12x^{2}-2x^{3}-8x^{2}
Multiply 2 and 4 to get 8.
16-24x+4x^{2}-2x^{3}
Combine 12x^{2} and -8x^{2} to get 4x^{2}.
2\left(2-x\right)^{3}-2x^{2}\times 4
Multiply x and x to get x^{2}.
2\left(8-12x+6x^{2}-x^{3}\right)-2x^{2}\times 4
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2-x\right)^{3}.
16-24x+12x^{2}-2x^{3}-2x^{2}\times 4
Use the distributive property to multiply 2 by 8-12x+6x^{2}-x^{3}.
16-24x+12x^{2}-2x^{3}-8x^{2}
Multiply 2 and 4 to get 8.
16-24x+4x^{2}-2x^{3}
Combine 12x^{2} and -8x^{2} to get 4x^{2}.
Examples
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Matrix
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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
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