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9x^{2}-12x+4-\left(2x-3\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-2\right)^{2}.
9x^{2}-12x+4-\left(4x^{2}-12x+9\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.
9x^{2}-12x+4-4x^{2}+12x-9
To find the opposite of 4x^{2}-12x+9, find the opposite of each term.
5x^{2}-12x+4+12x-9
Combine 9x^{2} and -4x^{2} to get 5x^{2}.
5x^{2}+4-9
Combine -12x and 12x to get 0.
5x^{2}-5
Subtract 9 from 4 to get -5.
9x^{2}-12x+4-\left(2x-3\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-2\right)^{2}.
9x^{2}-12x+4-\left(4x^{2}-12x+9\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.
9x^{2}-12x+4-4x^{2}+12x-9
To find the opposite of 4x^{2}-12x+9, find the opposite of each term.
5x^{2}-12x+4+12x-9
Combine 9x^{2} and -4x^{2} to get 5x^{2}.
5x^{2}+4-9
Combine -12x and 12x to get 0.
5x^{2}-5
Subtract 9 from 4 to get -5.