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3\left(x^{2}-6x+9\right)-6\left(3-x\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.
3x^{2}-18x+27-6\left(3-x\right)
Use the distributive property to multiply 3 by x^{2}-6x+9.
3x^{2}-18x+27-18+6x
Use the distributive property to multiply -6 by 3-x.
3x^{2}-18x+9+6x
Subtract 18 from 27 to get 9.
3x^{2}-12x+9
Combine -18x and 6x to get -12x.
3\left(x^{2}-6x+9\right)-6\left(3-x\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.
3x^{2}-18x+27-6\left(3-x\right)
Use the distributive property to multiply 3 by x^{2}-6x+9.
3x^{2}-18x+27-18+6x
Use the distributive property to multiply -6 by 3-x.
3x^{2}-18x+9+6x
Subtract 18 from 27 to get 9.
3x^{2}-12x+9
Combine -18x and 6x to get -12x.