( \frac { 1 } { 3 } x + \frac { 1 } { 3 } y ) ( - 3 x + 3 y
Evaluate
y^{2}-x^{2}
Expand
y^{2}-x^{2}
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\frac{1}{3}x\left(-3\right)x+\frac{1}{3}x\times 3y+\frac{1}{3}y\left(-3\right)x+\frac{1}{3}y\times 3y
Apply the distributive property by multiplying each term of \frac{1}{3}x+\frac{1}{3}y by each term of -3x+3y.
\frac{1}{3}x^{2}\left(-3\right)+\frac{1}{3}x\times 3y+\frac{1}{3}y\left(-3\right)x+\frac{1}{3}y\times 3y
Multiply x and x to get x^{2}.
\frac{1}{3}x^{2}\left(-3\right)+\frac{1}{3}x\times 3y+\frac{1}{3}y\left(-3\right)x+\frac{1}{3}y^{2}\times 3
Multiply y and y to get y^{2}.
\frac{-3}{3}x^{2}+\frac{1}{3}x\times 3y+\frac{1}{3}y\left(-3\right)x+\frac{1}{3}y^{2}\times 3
Multiply \frac{1}{3} and -3 to get \frac{-3}{3}.
-x^{2}+\frac{1}{3}x\times 3y+\frac{1}{3}y\left(-3\right)x+\frac{1}{3}y^{2}\times 3
Divide -3 by 3 to get -1.
-x^{2}+xy+\frac{1}{3}y\left(-3\right)x+\frac{1}{3}y^{2}\times 3
Cancel out 3 and 3.
-x^{2}+xy+\frac{-3}{3}yx+\frac{1}{3}y^{2}\times 3
Multiply \frac{1}{3} and -3 to get \frac{-3}{3}.
-x^{2}+xy-yx+\frac{1}{3}y^{2}\times 3
Divide -3 by 3 to get -1.
-x^{2}+\frac{1}{3}y^{2}\times 3
Combine xy and -yx to get 0.
-x^{2}+y^{2}
Cancel out 3 and 3.
\frac{1}{3}x\left(-3\right)x+\frac{1}{3}x\times 3y+\frac{1}{3}y\left(-3\right)x+\frac{1}{3}y\times 3y
Apply the distributive property by multiplying each term of \frac{1}{3}x+\frac{1}{3}y by each term of -3x+3y.
\frac{1}{3}x^{2}\left(-3\right)+\frac{1}{3}x\times 3y+\frac{1}{3}y\left(-3\right)x+\frac{1}{3}y\times 3y
Multiply x and x to get x^{2}.
\frac{1}{3}x^{2}\left(-3\right)+\frac{1}{3}x\times 3y+\frac{1}{3}y\left(-3\right)x+\frac{1}{3}y^{2}\times 3
Multiply y and y to get y^{2}.
\frac{-3}{3}x^{2}+\frac{1}{3}x\times 3y+\frac{1}{3}y\left(-3\right)x+\frac{1}{3}y^{2}\times 3
Multiply \frac{1}{3} and -3 to get \frac{-3}{3}.
-x^{2}+\frac{1}{3}x\times 3y+\frac{1}{3}y\left(-3\right)x+\frac{1}{3}y^{2}\times 3
Divide -3 by 3 to get -1.
-x^{2}+xy+\frac{1}{3}y\left(-3\right)x+\frac{1}{3}y^{2}\times 3
Cancel out 3 and 3.
-x^{2}+xy+\frac{-3}{3}yx+\frac{1}{3}y^{2}\times 3
Multiply \frac{1}{3} and -3 to get \frac{-3}{3}.
-x^{2}+xy-yx+\frac{1}{3}y^{2}\times 3
Divide -3 by 3 to get -1.
-x^{2}+\frac{1}{3}y^{2}\times 3
Combine xy and -yx to get 0.
-x^{2}+y^{2}
Cancel out 3 and 3.
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Limits
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