Evaluate
3\left(\left(x-1\right)^{2}-4y^{2}\right)
Expand
3x^{2}-6x-12y^{2}+3
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\left(3x+6y-3\right)\left(x-2y-1\right)
Use the distributive property to multiply 3 by x+2y-1.
3x^{2}-6xy-3x+6yx-12y^{2}-6y-3x+6y+3
Apply the distributive property by multiplying each term of 3x+6y-3 by each term of x-2y-1.
3x^{2}-3x-12y^{2}-6y-3x+6y+3
Combine -6xy and 6yx to get 0.
3x^{2}-6x-12y^{2}-6y+6y+3
Combine -3x and -3x to get -6x.
3x^{2}-6x-12y^{2}+3
Combine -6y and 6y to get 0.
\left(3x+6y-3\right)\left(x-2y-1\right)
Use the distributive property to multiply 3 by x+2y-1.
3x^{2}-6xy-3x+6yx-12y^{2}-6y-3x+6y+3
Apply the distributive property by multiplying each term of 3x+6y-3 by each term of x-2y-1.
3x^{2}-3x-12y^{2}-6y-3x+6y+3
Combine -6xy and 6yx to get 0.
3x^{2}-6x-12y^{2}-6y+6y+3
Combine -3x and -3x to get -6x.
3x^{2}-6x-12y^{2}+3
Combine -6y and 6y to get 0.
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}