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

1 answer

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:

\[ 5 \cdot 13 \]