Answer:
[tex]A-B=(5-3p^4)(25+15p^4+9p^8)[/tex]
Step-by-step explanation:
We have that: A=125 and [tex]b=27p^{12}[/tex].
Now we want to factor [tex]A-B=125-27p^{12}[/tex]
We need to rewrite as difference of cubes to get
[tex]5^3-(3p^4)^3[/tex]
Recall the difference of cube formula:
[tex]x^3-y^3=(x-y)(x^2+xy+y^2)[/tex]
Let x=5 and [tex](3p^4)[/tex]
Then:
[tex]5^3-(3p^4)^3=(5-3p^4)(5^2+5*3p^4+(3p^4)^2)[/tex]
[tex]5^3-(3p^4)^3=(5-3p^4)(25+15p^4+9p^8)[/tex]
