Factor
\left(x-2y\right)\left(2a-3b\right)^{2}
Evaluate
\left(x-2y\right)\left(2a-3b\right)^{2}
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\left(4x-8y\right)a^{2}+\left(-12bx+24by\right)a+9b^{2}x-18b^{2}y
Consider 4a^{2}x-12abx+9b^{2}x-8a^{2}y+24aby-18b^{2}y as a polynomial over variable a.
\left(2a-3b\right)\left(2ax-3bx+6by-4ay\right)
Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power \left(4x-8y\right)a^{2} and n divides the constant factor 9xb^{2}-18yb^{2}. One such factor is 2a-3b. Factor the polynomial by dividing it by this factor.
x\left(2a-3b\right)-2y\left(2a-3b\right)
Consider 2ax-3bx+6by-4ay. Do the grouping 2ax-3bx+6by-4ay=\left(2ax-3bx\right)+\left(6by-4ay\right), and factor out x in the first and -2y in the second group.
\left(2a-3b\right)\left(x-2y\right)
Factor out common term 2a-3b by using distributive property.
\left(x-2y\right)\left(2a-3b\right)^{2}
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}