(4x²+3x-8)+(4x²-7x) (4x²+3x-8)-(4x²-7x) (x²+2xy+y²)+(x²-y²) (x²+2xy+y²)-(x²-y²)

Let's simplify each of the expressions step by step. 1. **Expression 1: \((4x^2 + 3x - 8) + (4x^2 - 7x)\)** Combine like terms: \[ (4x^2 + 4x^2) + (3x - 7x) - 8 = 8x^2 - 4x - 8 \] 2. **Expression 2: \((4x^2 + 3x - 8) - (4x^2 - 7x)\)** Distribute the negative and combine like terms: \[ (4x^2 - 4x^2) + (3x + 7x) - 8 = 0 + 10x - 8 = 10x - 8 \] 3. **Expression 3: \((x^2 + 2xy + y^2) + (x^2 - y^2)\)** Combine like terms: \[ (x^2 + x^2) + 2xy + (y^2 - y^2) = 2x^2 + 2xy + 0 = 2x^2 + 2xy \] 4. **Expression 4: \((x^2 + 2xy + y^2) - (x^2 - y^2)\)** Distribute the negative and combine like terms: \[ (x^2 - x^2) + 2xy + (y^2 + y^2) = 0 + 2xy + 2y^2 = 2xy + 2y^2 \] ### Summary of Results: 1. \((4x^2 + 3x - 8) + (4x^2 - 7x) = 8x^2 - 4x - 8\) 2. \((4x^2 + 3x - 8) - (4x^2 - 7x) = 10x - 8\) 3. \((x^2 + 2xy + y^2) + (x^2 - y^2) = 2x^2 + 2xy\) 4. \((x^2 + 2xy + y^2) - (x^2 - y^2) = 2xy + 2y^2\)