Math Problem Statement

5(a+b)-3(b-a) 

Solution

To simplify the expression 5(a+b)3(ba)5(a+b) - 3(b-a):

  1. Distribute the terms inside the parentheses: 5(a+b)=5a+5b5(a+b) = 5a + 5b 3(ba)=3b+3a-3(b-a) = -3b + 3a

    The expression becomes: 5a+5b3b+3a5a + 5b - 3b + 3a

  2. Combine like terms:

    • Combine 5a5a and 3a3a: 5a+3a=8a5a + 3a = 8a
    • Combine 5b5b and 3b-3b: 5b3b=2b5b - 3b = 2b

    The simplified expression is: 8a+2b8a + 2b

Final Answer:

8a+2b8a + 2b

Do you want more explanation or have any specific questions?


Here are 5 questions to deepen understanding:

  1. How does the distributive property work in algebra?
  2. Why is it important to combine like terms in algebraic expressions?
  3. How would the result change if the signs in the original expression were different?
  4. Can this simplification be visualized geometrically, and if so, how?
  5. How do we verify that two algebraic expressions are equivalent?

Tip: Always double-check signs during distribution to avoid errors!

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification of Expressions
Distributive Property

Formulas

Distributive Property: a(b + c) = ab + ac

Theorems

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Suitable Grade Level

Grades 6-8