To solve the problem using the difference of squares identity [tex]\( a^2 - b^2 = (a + b)(a - b) \)[/tex], we first need to express the given polynomial [tex]\( 9x^2 - 49 \)[/tex] in the form [tex]\( a^2 - b^2 \)[/tex].
1. Start by comparing the given polynomial to the difference of squares form:
[tex]\[
9x^2 - 49
\][/tex]
2. Identify the squares:
- [tex]\( 9x^2 \)[/tex] is a perfect square, and [tex]\( 9x^2 = (3x)^2 \)[/tex].
- [tex]\( 49 \)[/tex] is also a perfect square, and [tex]\( 49 = 7^2 \)[/tex].
3. So, we can write:
[tex]\[
9x^2 - 49 = (3x)^2 - 7^2
\][/tex]
4. Now, we can see that it matches the identity [tex]\( a^2 - b^2 \)[/tex] where:
[tex]\[
a = 3x \quad \text{and} \quad b = 7
\][/tex]
Therefore, the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are:
[tex]\[
a = 3x \quad \text{and} \quad b = 7
\][/tex]
