factor this trinomial 8y^6-125z^3

Question

What is the trinomial factor for 8y^6-125z^3

Answer 1

Given 8y^6-125z^3

= (2y^2)^3-(5z)^3

Now it is in the form a^3-b^3.

a^3-b^3 = (a-b)(a^2+ab+b^2)

a = 2y^2, b = 5z

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

= (2y^2-5z)(4y^4+10zy^2+25z^2)

Factoring of 8y^6-125z^3 is (2y^2-5z)(4y^4+10zy^2+25z^2).