Evaluate
\frac{x\left(100-x\right)}{2}
Expand
-\frac{x^{2}}{2}+50x
Graph
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\left(-\frac{x}{2}+\frac{50\times 2}{2}\right)x
To add or subtract expressions, expand them to make their denominators the same. Multiply 50 times \frac{2}{2}.
\frac{-x+50\times 2}{2}x
Since -\frac{x}{2} and \frac{50\times 2}{2} have the same denominator, add them by adding their numerators.
\frac{-x+100}{2}x
Do the multiplications in -x+50\times 2.
\frac{\left(-x+100\right)x}{2}
Express \frac{-x+100}{2}x as a single fraction.
\frac{-x^{2}+100x}{2}
Use the distributive property to multiply -x+100 by x.
\left(-\frac{x}{2}+\frac{50\times 2}{2}\right)x
To add or subtract expressions, expand them to make their denominators the same. Multiply 50 times \frac{2}{2}.
\frac{-x+50\times 2}{2}x
Since -\frac{x}{2} and \frac{50\times 2}{2} have the same denominator, add them by adding their numerators.
\frac{-x+100}{2}x
Do the multiplications in -x+50\times 2.
\frac{\left(-x+100\right)x}{2}
Express \frac{-x+100}{2}x as a single fraction.
\frac{-x^{2}+100x}{2}
Use the distributive property to multiply -x+100 by x.
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}