4x³y + 4x²y - 10xy²
factored
all I can see is a common factor of 2xy
tell me what you get
i got 2xy(2x²+2x-5y)
correct
BTW, keep the same name for your posts.
You suddenly turned from Sam to Ashley.
To factor the expression 4x³y + 4x²y - 10xy², we can look for a common factor among the terms. In this case, all the terms have a common factor of 2xy.
Taking out the common factor:
2xy(2x² + 2x - 5y)
Now, let's focus on the expression inside the parentheses, 2x² + 2x - 5y. To further factor this trinomial, we need to find two binomials whose product is equal to the trinomial.
To factor the trinomial, we can use different factoring methods like trial and error or the quadratic formula. In this case, trial and error seems more appropriate.
We need to find two numbers that multiply to give the product of the leading coefficient (2) and the constant term (-5). The leading coefficient is 2, and the constant term is -5. Let's list out the factors of 2 and -5:
Factors of 2: ±1, ±2
Factors of -5: ±1, ±5
Now, we need to find a combination of these factors such that the sum of the products of the outer and inner terms is equal to the middle term (2x). After trying different combinations, we find that -1 and 5 work:
(2x² - x) + (5y - y)
Now, we can factor by grouping:
x(2x - 1) + y(5 - 1)
Finally, we can rewrite the factored expression as:
2xy(2x - 1) + y(5 - 1)
And that's the factored form of the expression 4x³y + 4x²y - 10xy².