this binomial can be factored as the product of a binomial and trinomial. Enter the binomial factor.

64y^15 + 125

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

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

4y^5+5

To factor the binomial 64y^15 + 125, we need to find two terms that can be multiplied together to give us this expression.

First, let's look at the perfect cubes: 64 and 125.

64 can be written as (4y)^3 and 125 can be written as (5)^3.

Therefore, the binomial factor is (4y + 5).

To factor the binomial 64y^15 + 125, we can use the formula for factoring a sum of cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2).

In this case, we have 64y^15 as the cube of (4y^5)^3 and 125 as the cube of 5^3.
Using the formula, we can express the binomial as:

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

Now, let's apply the formula:

(4y^5 + 5)((4y^5)^2 - (4y^5)(5) + 5^2)

Simplifying further:

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

So, the binomial factor is 4y^5 + 5.