Factor
3\left(2x-3y\right)\left(2x+3y\right)x^{2}
Evaluate
12x^{4}-27\left(xy\right)^{2}
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3\left(4x^{4}-9x^{2}y^{2}\right)
Factor out 3.
x^{2}\left(4x^{2}-9y^{2}\right)
Consider 4x^{4}-9x^{2}y^{2}. Factor out x^{2}.
\left(2x-3y\right)\left(2x+3y\right)
Consider 4x^{2}-9y^{2}. Rewrite 4x^{2}-9y^{2} as \left(2x\right)^{2}-\left(3y\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
3x^{2}\left(2x-3y\right)\left(2x+3y\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}