(x-7)(x+7)

Jasonbradley

2 min read

·

Jun 17, 2024

10

Share

Expanding the Expression: (x-7)(x+7)

The expression (x-7)(x+7) represents the product of two binomials. We can expand this expression using the FOIL method, which stands for First, Outer, Inner, Last.

Here's how it works:

1. First: Multiply the first terms of each binomial: x * x = x²
2. Outer: Multiply the outer terms of the binomials: x * 7 = 7x
3. Inner: Multiply the inner terms of the binomials: -7 * x = -7x
4. Last: Multiply the last terms of each binomial: -7 * 7 = -49

Now, we combine all the terms:

x² + 7x - 7x - 49

Notice that the 7x and -7x terms cancel each other out. This leaves us with:

x² - 49

This result, x² - 49, is a difference of squares.

Key takeaway: The expression (x-7)(x+7) expands to x² - 49. This demonstrates a common pattern in algebra where the product of a binomial with its conjugate results in a difference of squares.