Answer :
To solve the expression [tex]\(169q^2 - 1\)[/tex], we can use the concept of the difference of squares. The difference of squares formula states:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In our expression, [tex]\(169q^2 - 1\)[/tex], we can identify the parts to fit into the formula:
1. Notice that [tex]\(169q^2\)[/tex] can be rewritten as [tex]\((13q)^2\)[/tex] because [tex]\(169\)[/tex] is [tex]\(13^2\)[/tex].
2. The number [tex]\(1\)[/tex] is the same as [tex]\(1^2\)[/tex].
Now, applying the difference of squares formula:
- Let [tex]\(a = 13q\)[/tex]
- Let [tex]\(b = 1\)[/tex]
The expression [tex]\(169q^2 - 1\)[/tex] becomes:
[tex]\((13q)^2 - 1^2 = (13q - 1)(13q + 1)\)[/tex]
Thus, the factored form of the expression [tex]\(169q^2 - 1\)[/tex] is:
[tex]\((13q - 1)(13q + 1)\)[/tex]
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In our expression, [tex]\(169q^2 - 1\)[/tex], we can identify the parts to fit into the formula:
1. Notice that [tex]\(169q^2\)[/tex] can be rewritten as [tex]\((13q)^2\)[/tex] because [tex]\(169\)[/tex] is [tex]\(13^2\)[/tex].
2. The number [tex]\(1\)[/tex] is the same as [tex]\(1^2\)[/tex].
Now, applying the difference of squares formula:
- Let [tex]\(a = 13q\)[/tex]
- Let [tex]\(b = 1\)[/tex]
The expression [tex]\(169q^2 - 1\)[/tex] becomes:
[tex]\((13q)^2 - 1^2 = (13q - 1)(13q + 1)\)[/tex]
Thus, the factored form of the expression [tex]\(169q^2 - 1\)[/tex] is:
[tex]\((13q - 1)(13q + 1)\)[/tex]
