Final answer:
The difference of two squares is a binomial in the form a² - b² and can be factored using the formula (a + b)(a - b). This method requires identifying perfect squares within the expression and applying the factoring pattern. Factoring this expression is a key algebraic skill.
Step-by-step explanation:
The difference of two squares is a specific type of algebraic expression and it takes the form of a² - b². To factor this kind of binomial, we apply the formula (a + b)(a - b). This is possible because when two squared terms are subtracted, their product will always result in the difference of their squares.
To illustrate, let's factor x² - 36. Here, both x² and 36 are perfect squares. The square root of x² is x, and the square root of 36 is 6. Using the formula, we get (x + 6)(x - 6) as the factored form of x² - 36.
Factoring the difference of two squares is a fundamental skill in algebra that simplifies expressions and helps in solving equations. It's crucial to recognize patterns like this to factor binomials efficiently.