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:

$$81=9^2\text{and}16=4^2$$

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:

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

Therefore, we can write:

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

So, the product equal to $81-16$ is:

$$5\cdot 13$$