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:

$$(9-4)=5\text{and}(9+4)=13$$

Thus, we have:

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

So the product that equals $81-16$ is:

$$5\cdot 13$$