Verified answer

1) a*(a + b) - b*(a - b) = a² + ab - ab +b² = a² + b² = a² + b²

2) b*(a - b) + b*(b + c) = b*(a + b) - b*(b - c)

b*(a - b) + b*(b + c) = ab - b² + b² + bc = ab + bc

b*(a + b) - b*(b - c) = ab + b² - b² + bc = ab + bc = ab + bc