Math Problem Statement

225p²q² - 1

Solution

The expression 225p2q21225p^2q^2 - 1 can be factored using the difference of squares formula. The difference of squares formula states that a2b2=(ab)(a+b)a^2 - b^2 = (a - b)(a + b).

First, we recognize that 225p2q2225p^2q^2 is a perfect square, since:

225p2q2=(15pq)2225p^2q^2 = (15pq)^2

Next, we write the expression as a difference of squares:

225p2q21=(15pq)212225p^2q^2 - 1 = (15pq)^2 - 1^2

Using the difference of squares formula, we factor this expression:

(15pq)212=(15pq1)(15pq+1)(15pq)^2 - 1^2 = (15pq - 1)(15pq + 1)

So, the factored form of 225p2q21225p^2q^2 - 1 is:

(15pq1)(15pq+1)(15pq - 1)(15pq + 1)

Would you like further details or have any questions?

Here are 8 related questions to further explore this topic:

  1. How do you factor other expressions using the difference of squares formula?
  2. What is the general form of the difference of squares?
  3. Can you explain the process of identifying perfect squares in an expression?
  4. How do you recognize when to use the difference of squares in factoring?
  5. What are other examples of factoring differences of squares?
  6. How can the difference of squares be applied in solving quadratic equations?
  7. Are there other special factoring formulas similar to the difference of squares?
  8. How does factoring help in simplifying algebraic expressions?

Tip: Always look for common factors first before applying special factoring formulas.

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Math Problem Analysis

Mathematical Concepts

Difference of Squares
Factoring

Formulas

Difference of squares formula: a^2 - b^2 = (a - b)(a + b)

Theorems

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Suitable Grade Level

Grades 10-12