Evaluate
2x^{2}-4x-\frac{5}{2}
Expand
2x^{2}-4x-\frac{5}{2}
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\left(2x+2\times \frac{1}{2}\right)\left(x-\frac{5}{2}\right)
Use the distributive property to multiply 2 by x+\frac{1}{2}.
\left(2x+1\right)\left(x-\frac{5}{2}\right)
Cancel out 2 and 2.
2x^{2}+2x\left(-\frac{5}{2}\right)+x-\frac{5}{2}
Apply the distributive property by multiplying each term of 2x+1 by each term of x-\frac{5}{2}.
2x^{2}-5x+x-\frac{5}{2}
Cancel out 2 and 2.
2x^{2}-4x-\frac{5}{2}
Combine -5x and x to get -4x.
\left(2x+2\times \frac{1}{2}\right)\left(x-\frac{5}{2}\right)
Use the distributive property to multiply 2 by x+\frac{1}{2}.
\left(2x+1\right)\left(x-\frac{5}{2}\right)
Cancel out 2 and 2.
2x^{2}+2x\left(-\frac{5}{2}\right)+x-\frac{5}{2}
Apply the distributive property by multiplying each term of 2x+1 by each term of x-\frac{5}{2}.
2x^{2}-5x+x-\frac{5}{2}
Cancel out 2 and 2.
2x^{2}-4x-\frac{5}{2}
Combine -5x and x to get -4x.
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}