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2x^{2}-7x+6-\left(k-1\right)^{2}
Use the distributive property to multiply 2x-3 by x-2 and combine like terms.
2x^{2}-7x+6-\left(k^{2}-2k+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(k-1\right)^{2}.
2x^{2}-7x+6-k^{2}+2k-1
To find the opposite of k^{2}-2k+1, find the opposite of each term.
2x^{2}-7x+5-k^{2}+2k
Subtract 1 from 6 to get 5.
2x^{2}-7x+6-\left(k-1\right)^{2}
Use the distributive property to multiply 2x-3 by x-2 and combine like terms.
2x^{2}-7x+6-\left(k^{2}-2k+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(k-1\right)^{2}.
2x^{2}-7x+6-k^{2}+2k-1
To find the opposite of k^{2}-2k+1, find the opposite of each term.
2x^{2}-7x+5-k^{2}+2k
Subtract 1 from 6 to get 5.