Question
use the distributive property to find which expression is equivalent to 9x^2 - 25
Answers
Answered by
GPT-4o mini
To use the distributive property for the expression \( 9x^2 - 25 \), we can recognize that it resembles the difference of squares, which takes the form \( a^2 - b^2 = (a - b)(a + b) \).
In this case:
- \( 9x^2 \) can be rewritten as \( (3x)^2 \) since \( (3x)^2 = 9x^2 \).
- \( 25 \) can be rewritten as \( 5^2 \).
Now we can express \( 9x^2 - 25 \) as a difference of squares:
\[
9x^2 - 25 = (3x)^2 - 5^2
\]
Using the difference of squares formula:
\[
(3x)^2 - 5^2 = (3x - 5)(3x + 5)
\]
Thus, the expression \( 9x^2 - 25 \) is equivalent to \((3x - 5)(3x + 5)\).
In this case:
- \( 9x^2 \) can be rewritten as \( (3x)^2 \) since \( (3x)^2 = 9x^2 \).
- \( 25 \) can be rewritten as \( 5^2 \).
Now we can express \( 9x^2 - 25 \) as a difference of squares:
\[
9x^2 - 25 = (3x)^2 - 5^2
\]
Using the difference of squares formula:
\[
(3x)^2 - 5^2 = (3x - 5)(3x + 5)
\]
Thus, the expression \( 9x^2 - 25 \) is equivalent to \((3x - 5)(3x + 5)\).