Factor
3x\left(y-3\right)\left(y+1\right)
Evaluate
3x\left(y-3\right)\left(y+1\right)
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3\left(xy^{2}-2xy-3x\right)
Factor out 3.
x\left(y^{2}-2y-3\right)
Consider xy^{2}-2xy-3x. Factor out x.
a+b=-2 ab=1\left(-3\right)=-3
Consider y^{2}-2y-3. Factor the expression by grouping. First, the expression needs to be rewritten as y^{2}+ay+by-3. To find a and b, set up a system to be solved.
a=-3 b=1
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. The only such pair is the system solution.
\left(y^{2}-3y\right)+\left(y-3\right)
Rewrite y^{2}-2y-3 as \left(y^{2}-3y\right)+\left(y-3\right).
y\left(y-3\right)+y-3
Factor out y in y^{2}-3y.
\left(y-3\right)\left(y+1\right)
Factor out common term y-3 by using distributive property.
3x\left(y-3\right)\left(y+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}