Let’s simplify the given expression step by step. The expression is:

$-8x^2 + 8xy - y^2 + x^2 - xy + 7y^2$

Step 1: Group like terms

Group terms with the same variables and powers: $(-8x^2 + x^2) + (8xy - xy) + (-y^2 + 7y^2)$

Step 2: Combine the coefficients of like terms

1. Combine $x^2$ terms: $-8x^2 + x^2 = -7x^2$
2. Combine $xy$ terms: $8xy - xy = 7xy$
3. Combine $y^2$ terms: (-y^2 + 7y^