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:

a2b2=(ab)(a+b)

To apply this to the expression 8116, we first recognize that 81 and 16 are both perfect squares:

81=92and16=42

Now we can rewrite the expression 8116 as:

8116=9242

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

9242=(94)(9+4)

Now, we calculate the two factors:

94=5 9+4=13

Therefore, we can write:

8116=(94)(9+4)=513

In conclusion, the product equal to 8116 is:

8116=513