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Find the product: [tex](G+13)(G-13)[/tex]

A. [tex]2G^2 - 26[/tex]
B. [tex]2G^2 - 169[/tex]
C. [tex]G^2 - 169[/tex]
D. [tex]G^2 - 26G - 169[/tex]

Answer :

To find the product of [tex]\((G+13)(G-13)\)[/tex], you can use the difference of squares formula, which is an important algebraic identity. The difference of squares states that for any two terms [tex]\(a\)[/tex] and [tex]\(b\)[/tex], [tex]\((a + b)(a - b) = a^2 - b^2\)[/tex].

In this expression, we have:
- [tex]\(a = G\)[/tex]
- [tex]\(b = 13\)[/tex]

According to the difference of squares formula, the product becomes:

[tex]\[
(G + 13)(G - 13) = G^2 - 13^2
\][/tex]

Next, calculate [tex]\(13^2\)[/tex]:

[tex]\[
13^2 = 169
\][/tex]

Substitute back into the expression:

[tex]\[
G^2 - 169
\][/tex]

Therefore, the simplified product of [tex]\((G+13)(G-13)\)[/tex] is [tex]\(G^2 - 169\)[/tex].

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