Problem 63 Collect like terms. $$ -8+11... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 11: Problem 63

Collect like terms. $$ -8+11 a-5 b+6 a-7 b+7 $$

Short Answer

Expert verified

-1 + 17a - 12b.

Step by step solution

Identify Like Terms

Look for terms that have the same variable raised to the same power. The given expression is -8 + 11a - 5b + 6a - 7b + 7.The like terms are:- Constant terms: -8, 7 - a terms: 11a, 6a - b terms: -5b, -7b.

Combine Constant Terms

Add or subtract the constant terms. -8 + 7 = -1.

Combine 'a' Terms

Add or subtract the coefficients of the 'a' terms. 11a + 6a = 17a.

Combine 'b' Terms

Add or subtract the coefficients of the 'b' terms. -5b - 7b = -12b.

Write the Final Expression

Combine the simplified terms to write the final expression. -1 + 17a - 12b.

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Key Concepts

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

constants

Constants are the simplest parts of algebraic expressions. They are numbers on their own without any variables attached. In the given exercise, -8 and 7 are the constants. Constants do not change in value because there are no variables involved to alter their magnitude.
When simplifying an expression, you should first identify and then combine these constants. You do this by straightforward addition or subtraction.
For instance, combining -8 and 7 results in -1, which was done in Step 2 of your exercise solution.

coefficients

Coefficients are the numerical parts of terms that include variables. They are the numbers that multiply the variables. In the expression -8 + 11a - 5b + 6a - 7b + 7:
- 11 and 6 are coefficients of 'a'
- -5 and -7 are coefficients of 'b'.
To combine like terms, you will need to add or subtract these coefficients. For instance, adding the coefficients of 'a' in the given problem: 11a + 6a results in 17a.
Similarly, combining the coefficients of the 'b' terms: -5b - 7b gives -12b.

like terms

Like terms are terms that have the same variables raised to the same power. Only like terms can be combined through addition or subtraction. This means:
- Constant terms (like -8 and 7 in the exercise)
- Terms with the same variable (like 11a and 6a, or -5b and -7b)
In the exercise, the final step involves writing the combined expression by bringing all the simplified terms together. After combining, -1, 17a, and -12b are identified as the final simplified terms.
You get the result -1 + 17a - 12b, where constants, 'a' terms, and 'b' terms have been grouped and combined correctly.

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91影视

Collect like terms. $$ -8+11 a-5 b+6 a-7 b+7 $$

Short Answer

Step by step solution

Identify Like Terms

Combine Constant Terms

Combine 'a' Terms

Combine 'b' Terms

Write the Final Expression

Key Concepts

constants

coefficients

like terms

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