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9x^{2}-6x\left(y-3\right)+y^{2}-6y+9
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-3\right)^{2}.
9x^{2}-6xy+18x+y^{2}-6y+9
Use the distributive property to multiply -6x by y-3.
9x^{2}-6x\left(y-3\right)+y^{2}-6y+9
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-3\right)^{2}.
9x^{2}-6xy+18x+y^{2}-6y+9
Use the distributive property to multiply -6x by y-3.