x^2+2xy-15y^2
is this factorable?
still confused
well, how about (x+5y)(x-3y)
You just need two factors of 15 that differ by 2 in value; one added, the other subtracted.
To determine if the expression x^2 + 2xy - 15y^2 is factorable, we can look for two binomial expressions that multiply together to form the given expression. If such binomials exist, then the expression is factorable.
We can start by splitting the middle term (2xy) into two terms that have a common factor of the coefficient of x^2 (which is 1) and the coefficient of y^2 (which is -15).
The product of the coefficient of x^2 and the coefficient of y^2 is -15. We need to find two numbers that multiply to -15 and add up to the middle coefficient (2). The factors of -15 are (-1, 15), (1, -15), (-3, 5), and (3, -5). Among these options, (-3, 5) satisfy the condition because -3 + 5 = 2.
Now, we can split the middle term (2xy) using these factors:
x^2 + 2xy - 15y^2 = x^2 - 3xy + 5xy - 15y^2
Next, we group the terms:
(x^2 - 3xy) + (5xy - 15y^2)
Now, we can factor by grouping:
x(x - 3y) + 5y(x - 3y)
This simplifies to:
(x + 5y)(x - 3y)
Therefore, x^2 + 2xy - 15y^2 can be factored as (x + 5y)(x - 3y).
well, let's see... +5 * -3 = -15
that help?