Math Problem Statement
Which of the following expressions is equivalent to the expression below: -7(5a - b) + 3(-8b + a)?
Solution
Let's solve the given expression step by step.
We are given:
Step 1: Distribute the numbers outside the parentheses.
-
First, distribute to both and : Thus, the first part becomes:
-
Next, distribute to both and : Thus, the second part becomes:
Step 2: Combine like terms.
Now, combine the terms from both parts: Simplify:
Final expression:
This matches the last option in the list: .
Answer:
The correct option is .
Would you like further details or explanations? Here are five additional questions based on this problem:
- How do you handle distribution in more complex expressions with multiple variables?
- What happens when there are more than two sets of parentheses in an expression?
- How can combining like terms help simplify polynomial expressions?
- What role does the order of operations play in simplifying expressions like this one?
- How do you check if your simplified expression is equivalent to one of the answer choices?
Tip: Always perform distribution carefully, especially when dealing with negative signs!
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Math Problem Analysis
Mathematical Concepts
Algebra
Distributive Property
Combining Like Terms
Formulas
Distributive Property: a(b + c) = ab + ac
Theorems
Distributive Law of Multiplication
Suitable Grade Level
Grades 7-9