Factor x^2 - 3xy - 18y^2
I am not too sure if this is right, but any help is appreciated! Thanks!
(x – 6y) (x + 3y) is this correct?
yes, this is right.
yes, that is the correct answer. i need free homework help ASAP.
(x - 6y) (x + 3y)
x^2 + 3xy - 6xy - 18y^2
x^2 - 3xy - 18y^2 correct!
So can you get my free homework help please? in exchange for me helping you with your problem
no
To factor the expression x^2 - 3xy - 18y^2, we can use the factoring method known as "trial and error" or "decomposition." Here's how you can find the correct factors:
1. Write down the coefficient of the x^2 term (which is 1) and the coefficient of the constant term (which is -18).
2. Find two numbers whose product is equal to the product of these two coefficients. In this case, the product of 1 and -18 is -18.
- The potential pairs of numbers that multiply to give -18 are (-1, 18), (-2, 9), (1, -18), and (2, -9).
3. Look for the pair of numbers whose sum is equal to the coefficient of the xy term (which is -3). In this case, the pair is (2, -9) since 2 + (-9) = -7.
4. Rewrite the middle term (-3xy) using these two numbers as coefficients. This is known as the "decomposition" step.:
-3xy = 2xy - 9xy
5. Factor by grouping. Group the terms with common factors together:
x^2 + 2xy - 9xy - 18y^2
6. Factor each group separately:
x(x + 2y) - 9y(x + 2y)
7. Notice that (x + 2y) is a common factor in both terms:
(x - 9y)(x + 2y)
Therefore, the correct factored form of x^2 - 3xy - 18y^2 is (x - 9y)(x + 2y).
So, the answer you provided, (x – 6y)(x + 3y), is not correct. The correct factored form is (x - 9y)(x + 2y).