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 is given by the identity:

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

In the case of \(81 - 16\), we can rewrite this expression using squares. Notice that:

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

Thus, we can write:

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

Now, applying the difference of squares identity:

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

Calculating the individual terms gives us:

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

Therefore, we have:

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

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

\[ 5 \times 13 \]