1. Problem statement: Simplify the expressions for parts a, b, and c. 2. Part a: Simplify $2x + x(4x - 2) - 6$ - Use distributive property: $x(4x - 2) = 4x^2 - 2x$ - Substitute back: $2x + 4x^2 - 2x - 6$ - Combine like terms: $2x - 2x = \cancel{2x} - \cancel{2x} = 0$ - Result: $4x^2 - 6$ 3. Part b: Simplify $5a - b(b - a) - 5a$ - Use distributive property: $b(b - a) = b^2 - ab$ - Substitute back: $5a - (b^2 - ab) - 5a$ - Remove parentheses: $5a - b^2 + ab - 5a$ - Combine like terms: $5a - 5a = \cancel{5a} - \cancel{5a} = 0$ - Result: $ab - b^2$ 4. Part c: Simplify $4 + a(3a - a) - 2$ - Use distributive property: $a(3a - a) = 3a^2 - a^2$ - Simplify inside parentheses: $3a^2 - a^2 = 2a^2$ - Substitute back: $4 + 2a^2 - 2$ - Combine constants: $4 - 2 = 2$ - Result: $2a^2 + 2$