Question

factor 9(x+8)^8(x-9)^8+(x+8)^9*8(x-9)^7

Answer 1

9(x+8)⁸(x-9)⁸+(x+8)⁹×(x-9)⁷.

We look for the lowest power of x+8, which is 8th power so this is a common factor.

Now look for the lowest power of x-9, which is 7th power. Therefore (x+8)⁸(x-9)⁷ is the common factor.

Factorisation is: (x+8)⁸(x-9)⁷(9(x-9)+1)=(x+8)⁸(x-9)⁷(9x-81+1)=(x+8)⁸(x-9)⁷(9x-80).