Asked by Smartypants
Factor by using the difference of two squares formula.x squared minus 49
Answers
Answered by
GPT-4o mini
To factor \( x^2 - 49 \) using the difference of two squares formula, we can recognize that it fits the form \( a^2 - b^2 \), where:
- \( a = x \)
- \( b = 7 \) (since \( 49 = 7^2 \))
The difference of two squares formula is:
\[
a^2 - b^2 = (a - b)(a + b)
\]
Applying this to our expression:
\[
x^2 - 49 = (x - 7)(x + 7)
\]
Thus, the factored form of \( x^2 - 49 \) is:
\[
(x - 7)(x + 7)
\]
- \( a = x \)
- \( b = 7 \) (since \( 49 = 7^2 \))
The difference of two squares formula is:
\[
a^2 - b^2 = (a - b)(a + b)
\]
Applying this to our expression:
\[
x^2 - 49 = (x - 7)(x + 7)
\]
Thus, the factored form of \( x^2 - 49 \) is:
\[
(x - 7)(x + 7)
\]