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 to the expression $81-16$, we first recognize that $81$ and $16$ are both perfect squares:

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

Now we can rewrite the expression $81-16$ as:

$$81-16=9^2-4^2$$

Using the difference of squares identity, we can factor this as:

$$9^2-4^2=(9-4)(9+4)$$

Now, we calculate the two factors:

$$9-4=5$$ $$9+4=13$$

Therefore, we can write:

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

In conclusion, the product equal to $81-16$ is:

$$81-16=5\cdot 13$$