Simplifying exponential functions

Question

What rules would I have to refresh on to learn how to simplify this or can someone provide the process for this.

Answer 1

Hi Oscar,

This is just factoring out the GCF (Greatest Common Factor) from an expression with 2 terms. It might be easier to see what's happening if you let A=x+6 and B=x+3. Then your original expression is equal to

5A⁷B⁴ + 7A⁶B⁵

The GCF is A⁶B⁴, so factor it out to get

A⁶B⁴(5A + 7B)

Now 5A + 7B = 5(x+6) + 7(x+3) = 5x + 30 + 7x + 21 = 12x + 51 = 3(4x+17), so the expression is equal to

3(x+6)⁶(x+3)⁴(4x+17)