Evaluate
\frac{\left(100-x\right)\left(x+40\right)}{2}
Expand
-\frac{x^{2}}{2}+30x+2000
Graph
Share
Copied to clipboard
40\left(-\frac{1}{2}\right)x+2000+x\left(-\frac{1}{2}\right)x+50x
Apply the distributive property by multiplying each term of 40+x by each term of -\frac{1}{2}x+50.
40\left(-\frac{1}{2}\right)x+2000+x^{2}\left(-\frac{1}{2}\right)+50x
Multiply x and x to get x^{2}.
\frac{40\left(-1\right)}{2}x+2000+x^{2}\left(-\frac{1}{2}\right)+50x
Express 40\left(-\frac{1}{2}\right) as a single fraction.
\frac{-40}{2}x+2000+x^{2}\left(-\frac{1}{2}\right)+50x
Multiply 40 and -1 to get -40.
-20x+2000+x^{2}\left(-\frac{1}{2}\right)+50x
Divide -40 by 2 to get -20.
30x+2000+x^{2}\left(-\frac{1}{2}\right)
Combine -20x and 50x to get 30x.
40\left(-\frac{1}{2}\right)x+2000+x\left(-\frac{1}{2}\right)x+50x
Apply the distributive property by multiplying each term of 40+x by each term of -\frac{1}{2}x+50.
40\left(-\frac{1}{2}\right)x+2000+x^{2}\left(-\frac{1}{2}\right)+50x
Multiply x and x to get x^{2}.
\frac{40\left(-1\right)}{2}x+2000+x^{2}\left(-\frac{1}{2}\right)+50x
Express 40\left(-\frac{1}{2}\right) as a single fraction.
\frac{-40}{2}x+2000+x^{2}\left(-\frac{1}{2}\right)+50x
Multiply 40 and -1 to get -40.
-20x+2000+x^{2}\left(-\frac{1}{2}\right)+50x
Divide -40 by 2 to get -20.
30x+2000+x^{2}\left(-\frac{1}{2}\right)
Combine -20x and 50x to get 30x.
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}