From the list of factors find two numbers that when added together give -16 and when multiplied together give -225. -25 and 9 added together give -16 and multiplied together give -225 so rewrite these values back into the expression (splitting the middle term):
4(15x^2 - 25xy + 9xy - 15y^2)
Now take out the HIGHEST common factor between the two sets of terms:
4[5x(3x - 5y) + 3y(3x - 5y)]
Now refactor it by taking the terms that are still outside the brackets and factoring them against the terms inside the brackets (can only be done if both sets of brackets are identical):
Comments
Take out 4 as a common factor:
4(15x^2 - 16xy - 15y^2)
Multiply the value of 15x^2 (15) against the value of -15y^2 (-15):
15 * -15 = -225
Factors of -225 = +-(1, 3, 5, 9, 15, 25, 45, 75, 225)
From the list of factors find two numbers that when added together give -16 and when multiplied together give -225. -25 and 9 added together give -16 and multiplied together give -225 so rewrite these values back into the expression (splitting the middle term):
4(15x^2 - 25xy + 9xy - 15y^2)
Now take out the HIGHEST common factor between the two sets of terms:
4[5x(3x - 5y) + 3y(3x - 5y)]
Now refactor it by taking the terms that are still outside the brackets and factoring them against the terms inside the brackets (can only be done if both sets of brackets are identical):
4(5x + 3y)(3x - 5y)
That is now fully factorised.
The only immediately obvious common factor is 4. So you have
4 (15x^2 - 16xy + 15y^2)
Since no factorization into binomials comes to mind,
you can check via the quadratic formula: let y = 1 for a moment and you have
15 x^2 - 16 x + 15
If this had factors, it would have "zeros", i.e., solutions to the equation
15 x^2 - 16x + 15 = 0.
x = (16 plus or minus sqrt(256-900))/30
Doesn't work, because 256<900.
Therefore, there are no real factors beyond what I showed at line 2.
I know the correct answer but im not saying sorry. You should go and ask your teacher for help and tell her that your not getting it.
(6x-10y)(10x+6y)