Evaluate
\frac{\left(x-1\right)\left(4x+5\right)}{2}
Expand
2x^{2}+\frac{x}{2}-\frac{5}{2}
Graph
Share
Copied to clipboard
\frac{1}{2}\left(4x+3+2\right)\left(x-1\right)
Combine x and 3x to get 4x.
\frac{1}{2}\left(4x+5\right)\left(x-1\right)
Add 3 and 2 to get 5.
\left(\frac{1}{2}\times 4x+\frac{1}{2}\times 5\right)\left(x-1\right)
Use the distributive property to multiply \frac{1}{2} by 4x+5.
\left(\frac{4}{2}x+\frac{1}{2}\times 5\right)\left(x-1\right)
Multiply \frac{1}{2} and 4 to get \frac{4}{2}.
\left(2x+\frac{1}{2}\times 5\right)\left(x-1\right)
Divide 4 by 2 to get 2.
\left(2x+\frac{5}{2}\right)\left(x-1\right)
Multiply \frac{1}{2} and 5 to get \frac{5}{2}.
2x^{2}-2x+\frac{5}{2}x+\frac{5}{2}\left(-1\right)
Apply the distributive property by multiplying each term of 2x+\frac{5}{2} by each term of x-1.
2x^{2}+\frac{1}{2}x+\frac{5}{2}\left(-1\right)
Combine -2x and \frac{5}{2}x to get \frac{1}{2}x.
2x^{2}+\frac{1}{2}x-\frac{5}{2}
Multiply \frac{5}{2} and -1 to get -\frac{5}{2}.
\frac{1}{2}\left(4x+3+2\right)\left(x-1\right)
Combine x and 3x to get 4x.
\frac{1}{2}\left(4x+5\right)\left(x-1\right)
Add 3 and 2 to get 5.
\left(\frac{1}{2}\times 4x+\frac{1}{2}\times 5\right)\left(x-1\right)
Use the distributive property to multiply \frac{1}{2} by 4x+5.
\left(\frac{4}{2}x+\frac{1}{2}\times 5\right)\left(x-1\right)
Multiply \frac{1}{2} and 4 to get \frac{4}{2}.
\left(2x+\frac{1}{2}\times 5\right)\left(x-1\right)
Divide 4 by 2 to get 2.
\left(2x+\frac{5}{2}\right)\left(x-1\right)
Multiply \frac{1}{2} and 5 to get \frac{5}{2}.
2x^{2}-2x+\frac{5}{2}x+\frac{5}{2}\left(-1\right)
Apply the distributive property by multiplying each term of 2x+\frac{5}{2} by each term of x-1.
2x^{2}+\frac{1}{2}x+\frac{5}{2}\left(-1\right)
Combine -2x and \frac{5}{2}x to get \frac{1}{2}x.
2x^{2}+\frac{1}{2}x-\frac{5}{2}
Multiply \frac{5}{2} and -1 to get -\frac{5}{2}.
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}