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x^{2}-6x+6y
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x^{2}-6x+6y
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y^{2}+x^{2}-y^{2}-6\left(x-y\right)
Consider \left(x+y\right)\left(x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
x^{2}-6\left(x-y\right)
Combine y^{2} and -y^{2} to get 0.
x^{2}-6x+6y
Use the distributive property to multiply -6 by x-y.
y^{2}+x^{2}-y^{2}-6\left(x-y\right)
Consider \left(x+y\right)\left(x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
x^{2}-6\left(x-y\right)
Combine y^{2} and -y^{2} to get 0.
x^{2}-6x+6y
Use the distributive property to multiply -6 by x-y.
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