(x-6)(x+6) Answer

Jasonbradley

2 min read

·

Jun 17, 2024

17

Share

Understanding (x-6)(x+6)

This expression represents the product of two binomials: (x-6) and (x+6). It's a common example used to demonstrate the concept of the difference of squares.

The Difference of Squares Pattern

The difference of squares pattern states:

(a - b)(a + b) = a² - b²

In our case, 'a' is 'x' and 'b' is '6'.

Expanding the Expression

Let's expand (x-6)(x+6) using the distributive property (or FOIL method):

• First: x * x = x²
• Outer: x * 6 = 6x
• Inner: -6 * x = -6x
• Last: -6 * 6 = -36

Combining the terms, we get:

x² + 6x - 6x - 36

The middle terms (6x and -6x) cancel each other out, leaving us with:

x² - 36

Conclusion

Therefore, (x-6)(x+6) simplifies to x² - 36, demonstrating the difference of squares pattern.

This pattern is helpful for quickly factoring and expanding expressions and can be applied to various algebraic problems.