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The 'difference of squares' is a special type of polynomial. It looks like this: a^2 - b^2 . In this form, 'a' and 'b' represent any algebraic expressions. For the difference of squares to work, both parts must be perfect squares. For instance, in the given problem, p^2 q^2 - 100 , p^2 q^2 and 100 are both perfect squares: (pq)^2 and 10^2 , respectively. This makes them fit perfectly into the difference of squares formula. Understanding this concept helps in recognizing and solving these types of problems. This formula can be applied to many polynomial factors, making it a handy tool for algebraic factoring.

Algebraic expressions are combinations of variables, numbers, and operations. For example, in the given problem, p^2 q^2 - 100 , p^2 q^2 and 100 . An important part of algebra is understanding how to manipulate these expressions. These manipulations include operations such as:

• Addition
• Subtraction
• Multiplication
• Division

When factoring algebraic expressions, we break them down into simpler components or factors. This makes them easier to work with. Factoring can help in solving algebraic equations and simplifying expressions. It's like breaking a complicated problem into smaller, more manageable parts. In the example problem, we used the difference of squares to factor it. This demonstrates how recognizing patterns in algebraic expressions can lead to a solution.

Factoring techniques are methods used to break down algebraic expressions into simpler terms. One common technique is factoring the difference of squares. We've seen it in action: a^2 - b^2 = (a - b)(a + b) . When factoring, consider these steps:

• Identify the form: Look for perfect squares and determine if the expression fits a^2 - b^2
• Apply the formula: Use the (a - b)(a + b) formula
• Substitute: Replace 'a' and 'b' with identified values

This simplifies the problem significantly. The given problem, p^2 q^2 - 100 , follows these steps. We identified pq and 10 . This allowed us to use the difference of squares technique: (pq - 10)(pq + 10) . Mastering this and other factoring techniques empowers solving more complex algebraic problems effectively.