Question

Use the polynomial identity of the difference of two squares to write a product equal to 81−16 .

Answer 1

The difference of two squares can be expressed using the identity:

\[
a^2 - b^2 = (a - b)(a + b)
\]

In the case of \(81 - 16\), we recognize that \(81\) is \(9^2\) and \(16\) is \(4^2\). Thus, we can rewrite \(81 - 16\) as:

\[
81 - 16 = 9^2 - 4^2
\]

Applying the difference of squares identity:

\[
9^2 - 4^2 = (9 - 4)(9 + 4)
\]

Now we can simplify the terms inside the parentheses:

\[
(9 - 4) = 5 \quad \text{and} \quad (9 + 4) = 13
\]

Thus, we have:

\[
81 - 16 = (9 - 4)(9 + 4) = 5 \cdot 13
\]

So the product that equals \(81 - 16\) is:

\[
5 \cdot 13
\]