what is the binomial factor 64y^15+125

Question

This binomial can be factored as the product of a binomial and a trinomial, what is the binomial factor?

Answer 1

Given 64y^15+125

We are able to write it (4(y^5))^3+5^3

Now this is in the form of a^3+b^3

Recall the formula a^3+b^3 = (a+b)(a^2-ab+b^2)

a = 4y^5, b = 5

= (4y^5+5)[(4y^5)^2-(4y^5)5+5^2]

= (4y^5+5)(16y^10-20y^5+25)

 Factoring of 64y^15+125 = (4y^5+5)(16y^10-20y^5+25).