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
5 x y^2 (1 + 3x - 5 + 13 x) =5 x y^2 (2x+9)
5 x y^2 ( 16 x-4) = 5 x y^2 (2x+9)
20 x y^2 (4x-1) = 5 x y^2 (2x+9)
or
4(4x-1) = 2 x + 9
14 x = 13
To factor out the Greatest Common Factor (GCF) from each term in the equation, we need to find the common factors among the terms and then factor them out.
Let's break down the equation and identify the GCF of each term:
5xy^2:
The factors of 5 are 1 and 5.
The factors of x are x.
The factors of y^2 are y and y.
Therefore, the GCF of 5xy^2 is xy^2.
15x^2y^2:
The factors of 15 are 1, 3, 5, and 15.
The factors of x^2 are x and x.
The factors of y^2 are y and y.
Therefore, the GCF of 15x^2y^2 is 3xy^2.
-25xy^2:
The factors of -25 are -1, -5, 1, 5, -25, and 25.
The factors of x are x.
The factors of y^2 are y and y.
Therefore, the GCF of -25xy^2 is xy^2.
65x^2y^2:
The factors of 65 are 1, 5, 13, and 65.
The factors of x^2 are x and x.
The factors of y^2 are y and y.
Therefore, the GCF of 65x^2y^2 is 5x^2y^2.
Now, let's write the equation with the GCF factored out:
5xy^2 + 15x^2y^2 - 25xy^2 + 65x^2y^2 = 10x^2y^2 + 45xy^2
xy^2(5 + 15x - 25 + 65x) = 5x^2y^2(2 + 9)
Simplifying further:
xy^2(20x - 20) = 5x^2y^2(11)
Now we have factored out the GCF of each polynomial in the equation.