Question

We want to factor the following expression: 16x^6 + 24x^3y^5 + 9y^10 We can factor the expression as (U + V)^2 where U and V are either constant integers or single-variable expressions 1) What are U and V?

Answer 1

Given data:

The given expression is 16x^6+24x^3y^5+9y^10.

The given expression can be written as,

$\begin{gathered} 16x^6+24x^{3^{}}y^5+9y^{10}=(4x^3)^2+2(4x^3)(3y^5)+(3y^5)^2 \\ =(4x^3+3y^5)^2 \end{gathered}$

Thus, the value of U=4x^3, and V=3y^5.

The factors of the given expression is,

(4x^3+3y^5)(4x^3+3y^5).