14 d x - 42 d y - 6 p x + 18 p y + 2 x y - 6 y ^ { 2 }
Factor
2\left(x-3y\right)\left(y+7d-3p\right)
Evaluate
2\left(x-3y\right)\left(y+7d-3p\right)
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2\left(7dx-21dy-3px+9py+xy-3y^{2}\right)
Factor out 2.
x\left(y-3p+7d\right)-3y\left(y-3p+7d\right)
Consider 7dx-21dy-3px+9py+xy-3y^{2}. Do the grouping 7dx-21dy-3px+9py+xy-3y^{2}=\left(xy-3px+7dx\right)+\left(-3y^{2}+9py-21dy\right), and factor out x in the first and -3y in the second group.
\left(y-3p+7d\right)\left(x-3y\right)
Factor out common term y-3p+7d by using distributive property.
2\left(y-3p+7d\right)\left(x-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}