Answer:
4x² - 6x
Explanation:
First, you need to understand how a negative sign to the left of parentheses works.
Look at this example:
10 - 7 = 3
This is very simple. I'm sure you know that 10 - 7 = 3.
7 can be written as 5 + 2, so subtracting 7 from 10 is the same as subtracting 5 + 2 from 10.
Let's write that:
10 - (5 + 2)
Use the rules of the order of operations and add 5 + 2 in the parentheses first. Then do the subtraction.
10 - (5 + 2) = 10 - 7 = 3
We get 3 as we expected.
Now, instead of using the correct order of operations, we will use the distributive property and distribute the negative sign to the left of the (5 + 2).
10 - (5 + 2) = 10 - 5 - 2 = 5 - 2 = 3
Once again, we get 3.
The important thing is to realize that when you subtract a quantity inside parentheses, the negative sign to the left of the parentheses changes every sign inside the parentheses.
10 - (5 + 2) has a positive 5 and a positive 2 inside the parentheses.
When you distribute the negative sign, you now have
10 - 5 - 2
Now both the 5 and the 2 have negative signs.
Also, keep in mind that we can only combine like terms. Like terms are terms with exactly the same variable part.
Now let's do your problem.
(3x² + 2y² - 3x) + (2x² + y² - 2x) - (x² + 3y² + x) =
The parentheses around the first two expressions are unnecessary since they are being added. Just drop the first two sets of parentheses.
= 3x² + 2y² - 3x + 2x² + y² - 2x - (x² + 3y² + x)
Now we have to deal with a negative sign to the left of a set of parentheses. This is what we discussed above. To get rid of the last set of parentheses, we change every sign inside the parentheses.
= 3x² + 2y² - 3x + 2x² + y² - 2x - x² - 3y² - x
Now let's bring each set of like terms together before combining like terms.
= - 3x - 2x - x
= 3x² + 2x² - x² + 2y² + y² - 3y² - 3x - 2x - x
= 4x² - 6x