Question

4x^2+ 8xy - 60y^2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To factor the expression 4x^2 + 8xy - 60y^2, we can look for common factors and use the fact that the expression is a quadratic trinomial.

First, we can factor out a common factor of 4 from each term:
4x^2 + 8xy - 60y^2 = 4(x^2 + 2xy - 15y^2)

Now, we can focus on the quadratic trinomial x^2 + 2xy - 15y^2. We need to find two numbers that multiply to -15y^2 and add up to the coefficient of the middle term (which is 2).

The numbers that satisfy these conditions are 5y and -3y.
(x + 5y)(x - 3y)

So the factored form of 4x^2 + 8xy - 60y^2 is 4(x + 5y)(x - 3y).