Math Problem Statement

Simplify the following expressions: (10) -7a - (-2a + 4b) (11) 3a - (b + 5a) (12) (3a + 2) - (-a + 5)

Solution

I see the three problems presented in the image. Let's go through them one by one.

Problem (10):

7a(2a+4b)-7a - (-2a + 4b)

  1. Distribute the negative sign through the parentheses:
    7a(2a+4b)=7a+2a4b-7a - (-2a + 4b) = -7a + 2a - 4b
  2. Combine like terms:
    7a+2a=5a-7a + 2a = -5a Thus, the simplified expression is: 5a4b-5a - 4b

Problem (11):

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

  1. Distribute the negative sign through the parentheses:
    3a(b+5a)=3ab5a3a - (b + 5a) = 3a - b - 5a
  2. Combine like terms:
    3a5a=2a3a - 5a = -2a Thus, the simplified expression is: 2ab-2a - b

Problem (12):

(3a+2)(a+5)(3a + 2) - (-a + 5)

  1. Distribute the negative sign through the parentheses:
    (3a+2)(a+5)=3a+2+a5(3a + 2) - (-a + 5) = 3a + 2 + a - 5
  2. Combine like terms:
    3a+a=4a3a + a = 4a 25=32 - 5 = -3 Thus, the simplified expression is: 4a34a - 3

Would you like further clarification on any of these steps?

Here are 5 related questions to deepen your understanding:

  1. How do you handle distribution when there is a negative sign outside parentheses?
  2. What is the importance of combining like terms in algebraic expressions?
  3. How can you identify like terms quickly in complex expressions?
  4. What would happen if you incorrectly distribute a negative sign in an equation?
  5. Can these simplified expressions be factored further, and why or why not?

Tip: Always pay close attention to signs when distributing; small mistakes with negatives can lead to incorrect solutions!

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Expressions
Distribution
Combining Like Terms

Formulas

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

Theorems

Distributive Property
Associative Property of Addition

Suitable Grade Level

Grades 7-9