Factor
3\left(a-2b\right)\left(5c-3d\right)
Evaluate
3\left(a-2b\right)\left(5c-3d\right)
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3\left(5ac-3ad-10bc+6bd\right)
Factor out 3.
a\left(5c-3d\right)-2b\left(5c-3d\right)
Consider 5ac-3ad-10bc+6bd. Do the grouping 5ac-3ad-10bc+6bd=\left(5ac-3ad\right)+\left(-10bc+6bd\right), and factor out a in the first and -2b in the second group.
\left(5c-3d\right)\left(a-2b\right)
Factor out common term 5c-3d by using distributive property.
3\left(5c-3d\right)\left(a-2b\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}