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:

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

To apply this identity to the expression \(81 - 16\), we first identify \(a\) and \(b\). We notice that:

\[
81 = 9^2 \quad \text{and} \quad 16 = 4^2
\]

Thus, we can rewrite \(81 - 16\) as:

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

Now, we can apply the difference of squares identity:

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

Calculating the expressions gives:

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

Therefore, we can write:

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

So, the product equal to \(81 - 16\) is:

\[
5 \cdot 13
\]