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Chapter 4: Problem 79

Add or subtract as indicated. \((6 b+3 c)+(-2 b-8 c)\)

Short Answer

Expert verified
4b - 5c

Step by step solution

01

Identify Like Terms

Proceed by identifying like terms in the given algebraic expression. Like terms are those which have the same variable raised to the same power.
02

Group Like Terms

Group together the like terms from the expression (6b + 3c) and (-2b - 8c): (6b + (-2b)) + (3c + (-8c))
03

Perform Addition/Subtraction on Like Terms

Add or subtract the coefficients of the like terms separately: (6b - 2b) and (3c - 8c).
04

Simplify Each Set of Like Terms

Simplify (6b - 2b) = 4b and (3c - 8c) = -5c
05

Combine Simplified Like Terms

Combine the simplified terms to get the final answer: 4b - 5c

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Identifying Like Terms
In algebraic expressions, identifying like terms is the first crucial step. Like terms are terms that have the same variable raised to the same power. For example, in the expressions given, (6b + 3c) and (-2b - 8c), the terms 6b and -2b are like terms because they both have the variable 'b'. Similarly, 3c and -8c are like terms because they both have the variable 'c'.By identifying like terms, we can start grouping them to simplify the expression. Like terms can be easily combined because they essentially represent the same 'type' of quantity.
Grouping Like Terms
After identifying like terms, the next step is to group them together. This is important for simplification since we can handle each group separately. Consider the expression (6b + 3c) + (-2b - 8c) again. We can group the like terms: 6b and -2b are grouped together, and 3c and -8c are grouped together. The grouped expression looks like this: (6b + (-2b)) + (3c + (-8c)).Grouping helps to organize the expression, making it easier to perform operations on the like terms.
Simplifying Algebraic Expressions
Once like terms are grouped, simplifying algebraic expressions becomes straightforward. Simplification refers to adding or subtracting the coefficients of the like terms. For the grouped expression (6b + (-2b)) + (3c + (-8c)), perform the following operations:
  • Calculate 6b - 2b, which gives 4b.
  • Calculate 3c - 8c, which gives -5c.
Now combine the simplified results to get the final expression: 4b - 5c. By breaking the process into manageable steps and always working within the context of like terms, algebraic expressions can be simplified with ease.

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