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:

7(5ab)+3(8b+a)-7(5a - b) + 3(-8b + a)

Step 1: Distribute the numbers outside the parentheses.

  • First, distribute 7-7 to both 5a5a and b-b: 7×5a=35a,7×(b)=7b-7 \times 5a = -35a, \quad -7 \times (-b) = 7b Thus, the first part becomes: 35a+7b-35a + 7b

  • Next, distribute 33 to both 8b-8b and aa: 3×(8b)=24b,3×a=3a3 \times (-8b) = -24b, \quad 3 \times a = 3a Thus, the second part becomes: 24b+3a-24b + 3a

Step 2: Combine like terms.

Now, combine the terms from both parts: (35a+7b)+(24b+3a)=35a+3a+7b24b(-35a + 7b) + (-24b + 3a) = -35a + 3a + 7b - 24b Simplify: 35a+3a=32a,7b24b=17b-35a + 3a = -32a, \quad 7b - 24b = -17b

Final expression:

32a17b-32a - 17b

This matches the last option in the list: 32a17b-32a - 17b.

Answer:

The correct option is 32a17b-32a - 17b.

Would you like further details or explanations? Here are five additional questions based on this problem:

  1. How do you handle distribution in more complex expressions with multiple variables?
  2. What happens when there are more than two sets of parentheses in an expression?
  3. How can combining like terms help simplify polynomial expressions?
  4. What role does the order of operations play in simplifying expressions like this one?
  5. 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