Evaluate
\left(y-x\right)\left(6x-y\right)
Expand
-6x^{2}+7xy-y^{2}
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2xy-\left(6x^{2}-2xy-3yx+y^{2}\right)
Apply the distributive property by multiplying each term of 2x-y by each term of 3x-y.
2xy-\left(6x^{2}-5xy+y^{2}\right)
Combine -2xy and -3yx to get -5xy.
2xy-6x^{2}-\left(-5xy\right)-y^{2}
To find the opposite of 6x^{2}-5xy+y^{2}, find the opposite of each term.
2xy-6x^{2}+5xy-y^{2}
The opposite of -5xy is 5xy.
7xy-6x^{2}-y^{2}
Combine 2xy and 5xy to get 7xy.
2xy-\left(6x^{2}-2xy-3yx+y^{2}\right)
Apply the distributive property by multiplying each term of 2x-y by each term of 3x-y.
2xy-\left(6x^{2}-5xy+y^{2}\right)
Combine -2xy and -3yx to get -5xy.
2xy-6x^{2}-\left(-5xy\right)-y^{2}
To find the opposite of 6x^{2}-5xy+y^{2}, find the opposite of each term.
2xy-6x^{2}+5xy-y^{2}
The opposite of -5xy is 5xy.
7xy-6x^{2}-y^{2}
Combine 2xy and 5xy to get 7xy.
Examples
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Linear equation
y = 3x + 4
Arithmetic
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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}