Difference of Squares

In mathematics, the difference of squares is a specific form of factoring where a squared expression is subtracted from another squared expression. The difference of squares can be factored into the product of two binomials.

Formula for Difference of Squares

The formula for the difference of squares is:

a² - b² = (a + b)(a - b)

Where 'a' and 'b' are real numbers or algebraic expressions.

Examples of Difference of Squares

1. Factoring x² - 9:

x² - 9 = (x + 3)(x - 3)

2. Factoring 16y² - 25:

16y² - 25 = (4y + 5)(4y - 5)

Study Guide for Difference of Squares

To factor a difference of squares expression, follow these steps:

1. Identify the squared terms in the expression. These will be in the form of a² and b².
2. Write the expression in the form a² - b².
3. Factor the expression using the formula (a + b)(a - b).
4. Replace 'a' and 'b' with the square root of the squared terms in the original expression.
5. Simplify the expression if necessary.

Practice factoring different expressions using the difference of squares formula to master this concept.

Understanding the difference of squares can help in simplifying algebraic expressions and solving certain types of equations. It's an important concept to grasp for further studies in mathematics.

Hope this helps! Let me know if you have any other questions.