Evaluate
\left(2x-1\right)\left(x^{2}-x+7\right)
Expand
2x^{3}-3x^{2}+15x-7
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x^{3}+3x^{2}+3x+1+\left(x-2\right)^{3}
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.
x^{3}+3x^{2}+3x+1+x^{3}-6x^{2}+12x-8
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-2\right)^{3}.
2x^{3}+3x^{2}+3x+1-6x^{2}+12x-8
Combine x^{3} and x^{3} to get 2x^{3}.
2x^{3}-3x^{2}+3x+1+12x-8
Combine 3x^{2} and -6x^{2} to get -3x^{2}.
2x^{3}-3x^{2}+15x+1-8
Combine 3x and 12x to get 15x.
2x^{3}-3x^{2}+15x-7
Subtract 8 from 1 to get -7.
x^{3}+3x^{2}+3x+1+\left(x-2\right)^{3}
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.
x^{3}+3x^{2}+3x+1+x^{3}-6x^{2}+12x-8
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-2\right)^{3}.
2x^{3}+3x^{2}+3x+1-6x^{2}+12x-8
Combine x^{3} and x^{3} to get 2x^{3}.
2x^{3}-3x^{2}+3x+1+12x-8
Combine 3x^{2} and -6x^{2} to get -3x^{2}.
2x^{3}-3x^{2}+15x+1-8
Combine 3x and 12x to get 15x.
2x^{3}-3x^{2}+15x-7
Subtract 8 from 1 to get -7.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}