Question

How can 13 x 19 be rewritten using the
difference of two squares identity?
(1 point)
O (16 - 3) (16 + 3)
O (11 - 3) (11 + 3)
0 (10 + 3) (22 - 3)
0 (13 - 3) (19 + 3)

Answer 1

To rewrite \(13 \times 19\) using the difference of two squares identity, we can express the multiplication in the form of \( (a - b)(a + b) \), where \( a \) is the average of the two numbers and \( b \) is the half of the difference between the two numbers.

First, let's find \(a\) and \(b\):

1. Calculate \(a\):
\[
a = \frac{13 + 19}{2} = \frac{32}{2} = 16
\]

2. Calculate \(b\):
\[
b = \frac{19 - 13}{2} = \frac{6}{2} = 3
\]

Now we can rewrite \(13 \times 19\) as:
\[
(16 - 3)(16 + 3)
\]

Thus, the answer is:
\[
\boxed{(16 - 3)(16 + 3)}
\]