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.