Question

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

Answer 1

Answer:

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

Step-by-step 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:

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

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