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2x-2x^{2}+\left(2x-3\right)\left(x-1\right)
Use the distributive property to multiply 2x by 1-x.
2x-2x^{2}+2x^{2}-2x-3x+3
Apply the distributive property by multiplying each term of 2x-3 by each term of x-1.
2x-2x^{2}+2x^{2}-5x+3
Combine -2x and -3x to get -5x.
2x-5x+3
Combine -2x^{2} and 2x^{2} to get 0.
-3x+3
Combine 2x and -5x to get -3x.
2x-2x^{2}+\left(2x-3\right)\left(x-1\right)
Use the distributive property to multiply 2x by 1-x.
2x-2x^{2}+2x^{2}-2x-3x+3
Apply the distributive property by multiplying each term of 2x-3 by each term of x-1.
2x-2x^{2}+2x^{2}-5x+3
Combine -2x and -3x to get -5x.
2x-5x+3
Combine -2x^{2} and 2x^{2} to get 0.
-3x+3
Combine 2x and -5x to get -3x.