5xy^2 + 15x^2y^2 - 25xy^2 + 65x^2y^2 = 10x^2y^2 + 45xy^2
Factor out the GcF of each polynomial in the equation
To factor out the greatest common factor (GCF) from each polynomial in the equation, we need to first identify the common factors of each term.
Let's look at each term individually:
Term 1: 5xy^2
The factors of this term are: 5, x, y^2
Term 2: 15x^2y^2
The factors of this term are: 15, x^2, y^2
Term 3: -25xy^2
The factors of this term are: -25, x, y^2
Term 4: 65x^2y^2
The factors of this term are: 65, x^2, y^2
Now, let's find the GCF of these terms.
The GCF is the highest power of each common factor that appears in all terms. In this case, the GCF is x*y^2.
To factor out the GCF from each polynomial, divide each term by the GCF:
Term 1: (5xy^2) / (x*y^2) = 5
Term 2: (15x^2y^2) / (x*y^2) = 15x
Term 3: (-25xy^2) / (x*y^2) = -25
Term 4: (65x^2y^2) / (x*y^2) = 65x
Putting it all together, we have:
5xy^2 + 15x^2y^2 - 25xy^2 + 65x^2y^2 = (5 + 15x - 25 + 65x) * (x*y^2)
Simplifying further:
= (20 + 80x) * (x*y^2)
Therefore, the factored form of the given equation after factoring out the GCF of each polynomial is (20 + 80x) * (x*y^2).