Factor completely, then place the answer in the proper location on the grid. Write the answer in descending powers of x.
6x^4+15x^3y^2+3x^2y^3
x 3 - y 3
To factor the given expression completely, we can look for common factors among the terms. In this case, there is no common factor other than 1.
The given expression is: 6x^4 + 15x^3y^2 + 3x^2y^3
To facilitate factoring, let's assign each term a label:
Term 1: 6x^4
Term 2: 15x^3y^2
Term 3: 3x^2y^3
We can try factoring by grouping, which involves grouping terms together and factoring out the greatest common factor of each group.
First, let's group Term 1 and Term 2 together:
(6x^4 + 15x^3y^2)
The greatest common factor of these two terms is 3x^3, which we can factor out:
3x^3(2x + 5y^2)
Now, let's group Term 2 and Term 3 together:
(15x^3y^2 + 3x^2y^3)
The greatest common factor of these two terms is 3xy^2, which we can factor out:
3xy^2(5x + y)
Therefore, the factored expression becomes:
3x^3(2x + 5y^2) + 3xy^2(5x + y)
Now, let's rearrange the terms in descending powers of x:
3x^3(2x) + 3xy^2(5x) + 3x^3(5y^2) + 3xy^2(y)
Simplifying further, we get:
6x^4 + 15x^2y^2 + 15x^3y^2 + 3xy^3
Now, you can place the answer in the proper location on the grid.