Factor
a\left(a-1\right)\left(a+3\right)
Evaluate
a\left(a-1\right)\left(a+3\right)
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a\left(a^{2}+2a-3\right)
Factor out a.
p+q=2 pq=1\left(-3\right)=-3
Consider a^{2}+2a-3. Factor the expression by grouping. First, the expression needs to be rewritten as a^{2}+pa+qa-3. To find p and q, set up a system to be solved.
p=-1 q=3
Since pq is negative, p and q have the opposite signs. Since p+q is positive, the positive number has greater absolute value than the negative. The only such pair is the system solution.
\left(a^{2}-a\right)+\left(3a-3\right)
Rewrite a^{2}+2a-3 as \left(a^{2}-a\right)+\left(3a-3\right).
a\left(a-1\right)+3\left(a-1\right)
Factor out a in the first and 3 in the second group.
\left(a-1\right)\left(a+3\right)
Factor out common term a-1 by using distributive property.
a\left(a-1\right)\left(a+3\right)
Rewrite the complete factored expression.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}