How do you factor (p-5)^3+125(p−5)3+125?
1 Answer
Jan 23, 2016
Explanation:
The sum of cubes identity can be written:
a^3+b^3=(a+b)(a^2-ab+b^2)a3+b3=(a+b)(a2−ab+b2)
Here, we have
(p-5)^3+125(p−5)3+125
=(p-5)^3+5^3=(p−5)3+53
=((p-5)+5)((p-5)^2-(p-5)(5)+5^2)=((p−5)+5)((p−5)2−(p−5)(5)+52)
=p(p^2-10p+25-5p+25+25)=p(p2−10p+25−5p+25+25)
=p(p^2-15p+75)=p(p2−15p+75)
The internal quadratic
