1) a (a+b) -b (a-b) = a² + ab - ab + b² = a² + b²
2) 2a (a-b) -b (b-2a) = 2a² - 2ab - b² + 2ab = 2a² - b²
3) a (a² - 1) + a² (a - 1) = a * (a² -1 + a * (a-1)) = a * (a² - 1 + a² - a) = a * (2a² -1 - a) = a * (2a² - a - 1) = a * (2a² + a -2a -1) = a * (a* (2a+1) - (2a+1)) = a * (2a+1) * (a-1)
4) 5 (2a +ax) -5 (2a-ax) = 10a + 5ax -10a + 5ax = 10ax
5) 5x (x-2) - (4x² - 8) = 5x² - 10x -4x² +8 = x² - 10x + 8
6) 2 (x² - 7) + (7 - 2x²) = 2x² - 14 + 7 - 2x² = -7
7) 3x (x-y) + 3y (x+y) = 3 (x * (x-y) + y * (x+y)) = 3 (x² - xy + xy + y²) = 3 (x² + y²)
8) n² (n-2) - n (n² - 1) = n * (n * (n-2) - (n² -1)) = n * (n² - 2n -n² + 1) = n * (-2n+1)