Simplifying Question

Question

How do you simplify this?

 

4(x-5)³(x+6)⁷ + 7(x+6)⁶(x-5)⁴      

Answer 1

Factor it first, then simplify the factors.

 

f(x) = 4(x - 5)³(x + 6)⁷ + 7(x + 6)⁶(x - 5)⁴

 

Note the 2 terms have a common factor of (x - 5)³(x + 6)⁶

 

f(x) = (x - 5)³(x + 6)⁶ [4(x + 6) + 7(x - 5)]

 

Simplify the expression in [ ]

 

4(x + 6) + 7(x - 5) = (4 + 7)x + (24 - 35) = 11x - 11 = 11(x - 1)

 

f(x) = (x - 5)³(x + 6)⁶[11(x - 1)]

 

f(x) = 11(x - 1)(x - 5)³(x + 6)⁶

 

This is as simple as you can get.