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11x^{2}-5y^{2}
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11x^{2}-5y^{2}
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\left(3x-2y\right)^{2}-\left(2x-3y\right)^{2}-2x^{2}\left(-3\right)
Multiply x and x to get x^{2}.
9x^{2}-12xy+4y^{2}-\left(2x-3y\right)^{2}-2x^{2}\left(-3\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-2y\right)^{2}.
9x^{2}-12xy+4y^{2}-\left(4x^{2}-12xy+9y^{2}\right)-2x^{2}\left(-3\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3y\right)^{2}.
9x^{2}-12xy+4y^{2}-4x^{2}+12xy-9y^{2}-2x^{2}\left(-3\right)
To find the opposite of 4x^{2}-12xy+9y^{2}, find the opposite of each term.
5x^{2}-12xy+4y^{2}+12xy-9y^{2}-2x^{2}\left(-3\right)
Combine 9x^{2} and -4x^{2} to get 5x^{2}.
5x^{2}+4y^{2}-9y^{2}-2x^{2}\left(-3\right)
Combine -12xy and 12xy to get 0.
5x^{2}-5y^{2}-2x^{2}\left(-3\right)
Combine 4y^{2} and -9y^{2} to get -5y^{2}.
5x^{2}-5y^{2}-\left(-6x^{2}\right)
Multiply 2 and -3 to get -6.
5x^{2}-5y^{2}+6x^{2}
The opposite of -6x^{2} is 6x^{2}.
11x^{2}-5y^{2}
Combine 5x^{2} and 6x^{2} to get 11x^{2}.
\left(3x-2y\right)^{2}-\left(2x-3y\right)^{2}-2x^{2}\left(-3\right)
Multiply x and x to get x^{2}.
9x^{2}-12xy+4y^{2}-\left(2x-3y\right)^{2}-2x^{2}\left(-3\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-2y\right)^{2}.
9x^{2}-12xy+4y^{2}-\left(4x^{2}-12xy+9y^{2}\right)-2x^{2}\left(-3\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3y\right)^{2}.
9x^{2}-12xy+4y^{2}-4x^{2}+12xy-9y^{2}-2x^{2}\left(-3\right)
To find the opposite of 4x^{2}-12xy+9y^{2}, find the opposite of each term.
5x^{2}-12xy+4y^{2}+12xy-9y^{2}-2x^{2}\left(-3\right)
Combine 9x^{2} and -4x^{2} to get 5x^{2}.
5x^{2}+4y^{2}-9y^{2}-2x^{2}\left(-3\right)
Combine -12xy and 12xy to get 0.
5x^{2}-5y^{2}-2x^{2}\left(-3\right)
Combine 4y^{2} and -9y^{2} to get -5y^{2}.
5x^{2}-5y^{2}-\left(-6x^{2}\right)
Multiply 2 and -3 to get -6.
5x^{2}-5y^{2}+6x^{2}
The opposite of -6x^{2} is 6x^{2}.
11x^{2}-5y^{2}
Combine 5x^{2} and 6x^{2} to get 11x^{2}.
Examples
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{ 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}