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Chapter 5: Problem 25

Combine like terms. $$ 7 a+b-4 a-3 b $$

Short Answer

Expert verified
3a - 2b

Step by step solution

01

Identify like terms

To combine like terms, first identify the terms with the same variable. Here, the terms with the variable 'a' are 7a and -4a. The terms with the variable 'b' are b and -3b.
02

Combine like terms with the variable 'a'

Add the coefficients of the like terms with the variable 'a'. For 7a and -4a, the coefficients are 7 and -4. Combine them: \(7a - 4a = (7 - 4)a = 3a\).
03

Combine like terms with the variable 'b'

Next, add the coefficients of the like terms with the variable 'b'. For b and -3b, the coefficients are 1 and -3. Combine them: \(b - 3b = (1 - 3)b = -2b\).
04

Write the simplified expression

After combining the like terms, write down the simplified expression. The terms 3a and -2b are the remaining terms. Therefore, the simplified expression is \(3a - 2b\).

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Key Concepts

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

like terms
Understanding like terms is crucial in algebra. Like terms are terms that have the same variable raised to the same power. They can be combined with each other.

In the expression given in the exercise, we have: 7a, b, -4a, and -3b. Notice that:
  • The terms 7a and -4a are like terms because they both contain the variable a.
  • Similarly, b and -3b are like terms because they both contain the variable b.
To combine like terms, simply add or subtract their coefficients (the numerical part), and keep the variable part the same.
coefficients
Coefficients are the numerical part of terms that appear before the variable. They tell us how many times the variable is being multiplied.

For example, in the term 7a, the coefficient is 7. In the term -4a, the coefficient is -4. When we have terms likea or -3b, their coefficients are 1 and -3 respectively.

Combining like terms involves adding or subtracting the coefficients, while keeping the variable part unchanged. Here's how:
  • 7a - 4a = (7 - 4)a = 3a
  • b - 3b = (1 - 3)b = -2b
So the coefficients guide us in simplifying expressions.
simplified expression
A simplified expression is an expression where all like terms have been combined, and there are no further reductions possible. It's the cleanest form of the original expression.

To simplify an expression:
  • First, identify all like terms.
  • Second, combine the coefficients of these like terms.
  • Finally, write down the remaining simplified form.
For the exercise given, starting with 7a + b - 4a - 3b:
  • Combine 7a and -4a to get 3a.
  • Combine b and -3b to get -2b.
  • So, the simplified expression is 3a - 2b.
A simplified expression is easier to work with and understand.

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Most popular questions from this chapter

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