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2x^{2}+3x-\left(x-2\right)^{2}
Use the distributive property to multiply x by 2x+3.
2x^{2}+3x-\left(x^{2}-4x+4\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
2x^{2}+3x-x^{2}+4x-4
To find the opposite of x^{2}-4x+4, find the opposite of each term.
x^{2}+3x+4x-4
Combine 2x^{2} and -x^{2} to get x^{2}.
x^{2}+7x-4
Combine 3x and 4x to get 7x.
2x^{2}+3x-\left(x-2\right)^{2}
Use the distributive property to multiply x by 2x+3.
2x^{2}+3x-\left(x^{2}-4x+4\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
2x^{2}+3x-x^{2}+4x-4
To find the opposite of x^{2}-4x+4, find the opposite of each term.
x^{2}+3x+4x-4
Combine 2x^{2} and -x^{2} to get x^{2}.
x^{2}+7x-4
Combine 3x and 4x to get 7x.