Answer :
To solve the problem of multiplying [tex]\((13x + 7)(13x - 7)\)[/tex], we use a special algebraic identity known as the difference of squares. This identity states that:
[tex]\((a + b)(a - b) = a^2 - b^2\)[/tex].
In our problem, let:
- [tex]\(a = 13x\)[/tex]
- [tex]\(b = 7\)[/tex]
Now, apply the identity:
1. Calculate [tex]\(a^2\)[/tex]:
- [tex]\(a = 13x\)[/tex]
- So, [tex]\(a^2 = (13x)^2 = 169x^2\)[/tex]
2. Calculate [tex]\(b^2\)[/tex]:
- [tex]\(b = 7\)[/tex]
- So, [tex]\(b^2 = 7^2 = 49\)[/tex]
3. Apply the difference of squares formula:
- [tex]\(a^2 - b^2 = 169x^2 - 49\)[/tex]
By simplifying the expression [tex]\((13x + 7)(13x - 7)\)[/tex] using the difference of squares, we obtain the result:
[tex]\[
169x^2 - 49
\][/tex]
That's your answer!
[tex]\((a + b)(a - b) = a^2 - b^2\)[/tex].
In our problem, let:
- [tex]\(a = 13x\)[/tex]
- [tex]\(b = 7\)[/tex]
Now, apply the identity:
1. Calculate [tex]\(a^2\)[/tex]:
- [tex]\(a = 13x\)[/tex]
- So, [tex]\(a^2 = (13x)^2 = 169x^2\)[/tex]
2. Calculate [tex]\(b^2\)[/tex]:
- [tex]\(b = 7\)[/tex]
- So, [tex]\(b^2 = 7^2 = 49\)[/tex]
3. Apply the difference of squares formula:
- [tex]\(a^2 - b^2 = 169x^2 - 49\)[/tex]
By simplifying the expression [tex]\((13x + 7)(13x - 7)\)[/tex] using the difference of squares, we obtain the result:
[tex]\[
169x^2 - 49
\][/tex]
That's your answer!
