Question

A=125 and b= 27p12. What is the factored form of a-b

Answer 1

`A-B=(5-3p^4)(25+15p^4+9p^8)`

Explanation:

We have that: A=125 and
`b=27p^(12)`.

Now we want to factor
`A-B=125-27p^(12)`

We need to rewrite as difference of cubes to get

`5^3-(3p^4)^3`

Recall the difference of cube formula:

`x^3-y^3=(x-y)(x^2+xy+y^2)`

Let x=5 and
`(3p^4)`

Then:

`5^3-(3p^4)^3=(5-3p^4)(5^2+5*3p^4+(3p^4)^2)`

`5^3-(3p^4)^3=(5-3p^4)(25+15p^4+9p^8)`