What are the like terms in the exprression 3ac = ab - ac = 2ab? Explain.
Simplify the expression. Show your work.
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Simplify: 3ac - ab - ac - 2ab
To identify the like terms in the expression 3ac = ab - ac = 2ab, we need to understand what like terms are. Like terms are terms that have the same variables raised to the same exponents.
In this expression, we have three terms: 3ac, ab - ac, and 2ab. Let's break it down to identify the like terms:
1. 3ac: This term consists of the variables a and c, where a is raised to the power of 1 and c is also raised to the power of 1.
2. ab - ac: This is a combination of two terms (ab and -ac) separated by the subtraction sign. Both terms have the variable a raised to the power of 1, and they both contain the variable b raised to the power of 1 as well. Therefore, ab - ac is considered one term.
3. 2ab: This term contains the variables a and b, where a is raised to the power of 1 and b is also raised to the power of 1.
So, the like terms in the given expression are 3ac and 2ab, as they both have the same variables raised to the same exponents.
To simplify the expression, we can combine the like terms:
3ac + 2ab = (3a)c + (2a)b = ac + ab
Therefore, the simplified expression is ac + ab.