Evaluate
4x\left(5-x\right)
Expand
20x-4x^{2}
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4x^{2}-4x+1-2\left(2x-3\right)^{2}+17
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-1\right)^{2}.
4x^{2}-4x+1-2\left(4x^{2}-12x+9\right)+17
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.
4x^{2}-4x+1-8x^{2}+24x-18+17
Use the distributive property to multiply -2 by 4x^{2}-12x+9.
-4x^{2}-4x+1+24x-18+17
Combine 4x^{2} and -8x^{2} to get -4x^{2}.
-4x^{2}+20x+1-18+17
Combine -4x and 24x to get 20x.
-4x^{2}+20x-17+17
Subtract 18 from 1 to get -17.
-4x^{2}+20x
Add -17 and 17 to get 0.
4x^{2}-4x+1-2\left(2x-3\right)^{2}+17
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-1\right)^{2}.
4x^{2}-4x+1-2\left(4x^{2}-12x+9\right)+17
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.
4x^{2}-4x+1-8x^{2}+24x-18+17
Use the distributive property to multiply -2 by 4x^{2}-12x+9.
-4x^{2}-4x+1+24x-18+17
Combine 4x^{2} and -8x^{2} to get -4x^{2}.
-4x^{2}+20x+1-18+17
Combine -4x and 24x to get 20x.
-4x^{2}+20x-17+17
Subtract 18 from 1 to get -17.
-4x^{2}+20x
Add -17 and 17 to get 0.
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}