` a) ` ` (a + b)^2 - (a - b)^2 `
` = a^2 + 2ab + b^2 - (a^2 - 2ab + b^2) `
` = a^2 + 2ab + b^2 - a^2 + 2ab - b^2 `
` = 4ab `
` b) ` ` (a + b)^3 - (a - b)^3 - 2b^3 `
` = a^3 + 3a^{2}b + 3ab^{2} + b^3 - (a^3 - 3a^{2}b + 3ab^{3} - b^3) - 2b^3 `
` = a^3 + 3a^{2}b + 3ab^{2} + b^3 - a^3 + 3a^{2}b - 3ab^{3} + b^3 - 2b^3 `
` = 6a^{2}b `
` c) ` ` (x + y + z)^2 - 2(x + y + z)(x + y) + (x + y)^2 `
` = x^2 + y^2 + z^2 + xy + yz + zx - 2(x^2 + xy + xy + y^2 + zx + yz) + x^2 + 2xy + y^2 `
` = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx - 2x^2 - 2xy - 2xy - 2y^2 - 2zx - 2yz + x^2 + 2xy + y^2 `
` = z^2 `
