Math Problem Statement

Simplify the expression (2a^2 - 8) ÷ (2a - 4) at a = 2.

Solution

The expression in the image is:

2a282a4\frac{2a^2 - 8}{2a - 4}

You are likely being asked to simplify this expression.

Step-by-step simplification:

  1. Factor the numerator 2a282a^2 - 8: 2a28=2(a24)=2(a2)(a+2)2a^2 - 8 = 2(a^2 - 4) = 2(a - 2)(a + 2) This is a difference of squares.

  2. Factor the denominator 2a42a - 4: 2a4=2(a2)2a - 4 = 2(a - 2)

  3. Now rewrite the expression: 2(a2)(a+2)2(a2)\frac{2(a - 2)(a + 2)}{2(a - 2)}

  4. Cancel out the common terms 2(a2)2(a - 2) from both numerator and denominator: a+2a + 2

Thus, the simplified expression is:

a+2a + 2

Final Answer: a+2a + 2

Would you like further clarification on this, or do you have any questions?

Here are five related questions for practice:

  1. What is the general rule for factoring differences of squares?
  2. How would you simplify x29x3\frac{x^2 - 9}{x - 3}?
  3. What happens when a numerator or denominator cannot be factored?
  4. How can you check if your simplified expression is correct?
  5. What is the difference between factoring and simplifying?

Tip: Always look for common factors to cancel out when simplifying rational expressions!

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Rational Expressions
Factoring

Formulas

Factoring Difference of Squares
Simplifying Fractions

Theorems

Difference of Squares Theorem

Suitable Grade Level

Grades 8-10