Math Problem Statement

Which of the following expressions could be factored, with whole numbers only, using the difference of two squares?

Which of the following expressions could be factored, with whole numbers only, using the difference of two squares?

Solution

To determine which expressions can be factored using the difference of two squares, recall the standard form:

a2b2=(ab)(a+b)a^2 - b^2 = (a - b)(a + b)

Key criteria for factoring using the difference of squares:

  1. The expression must be a subtraction (difference), not addition.
  2. Both terms must be perfect squares (i.e., squares of whole numbers).

If you provide the specific expressions, I can analyze each one to see if they meet these criteria.

Would you like to list the expressions, or upload an image with them?


5 Related Questions:

  1. What are common examples of perfect squares?
  2. How do you factor a sum of squares if it’s possible?
  3. Can the difference of squares apply to polynomials with more than two terms?
  4. What happens if one term is not a perfect square?
  5. How is the difference of squares related to quadratic equations?

Tip: Always check for a greatest common factor (GCF) before applying the difference of squares—it can simplify the factoring process.

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Math Problem Analysis

Mathematical Concepts

Algebra
Factoring
Difference of Squares

Formulas

a^2 - b^2 = (a - b)(a + b)

Theorems

Difference of Squares Theorem

Suitable Grade Level

Grades 8-10