Answer:
Factors: (x²y+6)(y²-11)
Step-by-step explanation:
Here's the original equation.
x²y³ - 11x²y + 6y² - 66
Let's separate it into two groups to make it easier.
(x²y³ - 11x²y) + (6y² - 66)
Let's take a look at (x²y³ - 11x²y) first. Do we notice anything that can be removed from the parentheses?
Yes, x²y can be taken from both polynomials to simplify the contents of the parentheses.
Both polynomials have x² and both have at least one y. Combine that to get x²y. That means that within the parentheses y² and - 11 will be left.
So (x²y³ - 11x²y) becomes x²y (y²-11)
This works because if we multiply x²y * (y² - 11) we get (x²y³ - 11x²)
Let's apply this same idea to (6y² - 66).
6 is the only thing in common between the two polynomials.
If we follow the same steps we get 6 (y²-11).
Notice how when we simplified both groups they each had something on the outside and (y² - 11) in the parentheses?
So lets combine the things that were on the outside of both (y² - 11).
What was on the outside of each? x²y was on the outside for the first one, and 6 for the outside of the second one.
This means that if we combine everything and simplify, the factors we have are (x²y+6)(y²-11).
If you want to confirm, work your way backwards using the distributive property. You'll find that when you multiply (x²y+6) * (y² -11) you'll get = x²y³ - 11x²y + 6y² - 66. That was the original equation, so we know that these are the factors.
Hope that helps!
