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9y^{2}-7x^{2}
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9y^{2}-7x^{2}
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9xy-3x^{2}-\left(4x-3y\right)\left(x+3y\right)
Use the distributive property to multiply 3x by 3y-x.
9xy-3x^{2}-\left(4x^{2}+12xy-3yx-9y^{2}\right)
Apply the distributive property by multiplying each term of 4x-3y by each term of x+3y.
9xy-3x^{2}-\left(4x^{2}+9xy-9y^{2}\right)
Combine 12xy and -3yx to get 9xy.
9xy-3x^{2}-4x^{2}-9xy-\left(-9y^{2}\right)
To find the opposite of 4x^{2}+9xy-9y^{2}, find the opposite of each term.
9xy-3x^{2}-4x^{2}-9xy+9y^{2}
The opposite of -9y^{2} is 9y^{2}.
9xy-7x^{2}-9xy+9y^{2}
Combine -3x^{2} and -4x^{2} to get -7x^{2}.
-7x^{2}+9y^{2}
Combine 9xy and -9xy to get 0.
9xy-3x^{2}-\left(4x-3y\right)\left(x+3y\right)
Use the distributive property to multiply 3x by 3y-x.
9xy-3x^{2}-\left(4x^{2}+12xy-3yx-9y^{2}\right)
Apply the distributive property by multiplying each term of 4x-3y by each term of x+3y.
9xy-3x^{2}-\left(4x^{2}+9xy-9y^{2}\right)
Combine 12xy and -3yx to get 9xy.
9xy-3x^{2}-4x^{2}-9xy-\left(-9y^{2}\right)
To find the opposite of 4x^{2}+9xy-9y^{2}, find the opposite of each term.
9xy-3x^{2}-4x^{2}-9xy+9y^{2}
The opposite of -9y^{2} is 9y^{2}.
9xy-7x^{2}-9xy+9y^{2}
Combine -3x^{2} and -4x^{2} to get -7x^{2}.
-7x^{2}+9y^{2}
Combine 9xy and -9xy 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}