Evaluate
5\left(x^{2}-1\right)
Factor
5\left(x-1\right)\left(x+1\right)
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x^{2}+7x+10+4x^{2}-12x+5x-15
Combine 5x and 2x to get 7x.
5x^{2}+7x+10-12x+5x-15
Combine x^{2} and 4x^{2} to get 5x^{2}.
5x^{2}-5x+10+5x-15
Combine 7x and -12x to get -5x.
5x^{2}+10-15
Combine -5x and 5x to get 0.
5x^{2}-5
Subtract 15 from 10 to get -5.
5x^{2}-5
Multiply and combine like terms.
5\left(x^{2}-1\right)
Factor out 5.
\left(x-1\right)\left(x+1\right)
Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
5\left(x-1\right)\left(x+1\right)
Rewrite the complete factored expression.
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}