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2x^{2}-3x+3
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2x^{2}-3x+3
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3\left(x^{2}-2x+1\right)+x\left(3-x\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
3x^{2}-6x+3+x\left(3-x\right)
Use the distributive property to multiply 3 by x^{2}-2x+1.
3x^{2}-6x+3+3x-x^{2}
Use the distributive property to multiply x by 3-x.
3x^{2}-3x+3-x^{2}
Combine -6x and 3x to get -3x.
2x^{2}-3x+3
Combine 3x^{2} and -x^{2} to get 2x^{2}.
3\left(x^{2}-2x+1\right)+x\left(3-x\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
3x^{2}-6x+3+x\left(3-x\right)
Use the distributive property to multiply 3 by x^{2}-2x+1.
3x^{2}-6x+3+3x-x^{2}
Use the distributive property to multiply x by 3-x.
3x^{2}-3x+3-x^{2}
Combine -6x and 3x to get -3x.
2x^{2}-3x+3
Combine 3x^{2} and -x^{2} to get 2x^{2}.
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