Decomposition factor (a + x) ^ (M + 1) (B + x) ^ (n-1) - (a + x) ^ m (B + x) ^ n=

Decomposition factor (a + x) ^ (M + 1) (B + x) ^ (n-1) - (a + x) ^ m (B + x) ^ n=

=(a+x)^m(b+x)^(n-1) [(a+x)-(b+x)]
=(a-b)(a+x)^m(b+x)^(n-1)

[(x + y) square - (X-Y) square] / (2XY), where x = 10 and y = 5

X squared + y squared + 2XY = 10, X squared + y squared - 2XY = 6, so x squared + y squared = (10 + 6) / 2 = 8, 2XY is equal to 2

The square of 5 (X-Y) + the square of 10 (Y-X) need to use decomposition factor
The first one should be 5 (the cube of X-Y is wrong

5(x-y)^3+10(y-x)^2
=5(x-y)^3+10(x-y)^2
=5(x-y)^2[(x-y)+2]