Evaluate
x\left(x-2y\right)+x^{2}-y^{2}
Expand
2x^{2}-2xy-y^{2}
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x^{2}-y^{2}+x\left(x-2y\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}-y^{2}+x^{2}-2xy
Use the distributive property to multiply x by x-2y.
2x^{2}-y^{2}-2xy
Combine x^{2} and x^{2} to get 2x^{2}.
x^{2}-y^{2}+x\left(x-2y\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}-y^{2}+x^{2}-2xy
Use the distributive property to multiply x by x-2y.
2x^{2}-y^{2}-2xy
Combine x^{2} and x^{2} to get 2x^{2}.
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