Find the sum of (-3a+4cd-6ac)-(7ab-9cd-10ac)+(-8ab+cd-2ac)-(9ab-5cd+CD)
pay attention to which variables are paired together, and just add up like terms. For example, the cd terms are
4-(-9)+1-1 = 13cd
To find the sum of the given expressions, we can simplify each expression individually and then add them together.
Given expression: (-3a+4cd-6ac)-(7ab-9cd-10ac)+(-8ab+cd-2ac)-(9ab-5cd+CD)
First, let's simplify each expression within the parentheses:
Expression 1: (-3a+4cd-6ac)
- No similar terms to combine.
Expression 2: (7ab-9cd-10ac)
- No similar terms to combine.
Expression 3: (-8ab+cd-2ac)
- No similar terms to combine.
Expression 4: (9ab-5cd+CD)
- We see the term "CD" which may not be a similar term to other terms because of the difference in case. To properly combine like terms, we need to convert all variables to either uppercase or lowercase. Let's assume that the variables should be lowercase. So, we can rewrite this expression as (9ab-5cd+cd).
Now, let's combine similar terms for each expression:
Expression 1: (-3a+4cd-6ac)
Expression 2: (7ab-9cd-10ac)
Expression 3: (-8ab+cd-2ac)
Expression 4: (9ab-5cd+cd)
= 9ab - 5cd + cd
= 9ab - 4cd
Now, let's add all the simplified expressions together:
(-3a+4cd-6ac) - (7ab-9cd-10ac) + (-8ab+cd-2ac) - (9ab-5cd+CD)
= (-3a+4cd-6ac) + (-(7ab-9cd-10ac)) + (-8ab+cd-2ac) + (9ab-4cd)
Remember, when we have a negative sign before parentheses, we need to distribute the negative sign to all the terms within the parentheses:
= -3a + 4cd - 6ac - 7ab + 9cd + 10ac - 8ab + cd - 2ac + 9ab - 4cd
Now, let's combine like terms:
= (-3a - 7ab - 8ab + 9ab) + (4cd + 9cd - 4cd) + (-6ac + 10ac - 2ac) + (cd)
= -9a + 4cd + 3cd + 2cd - 4ac + 8ac + cd
= -9a + 9cd + 6cd + 8ac + cd
= -9a + 15cd + 8ac
Therefore, the sum of the given expression (-3a+4cd-6ac)-(7ab-9cd-10ac)+(-8ab+cd-2ac)-(9ab-5cd+CD) is -9a + 15cd + 8ac.