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)

In the case of 8116, we recognize that 81 is 92 and 16 is 42. Thus, we can rewrite 8116 as:

8116=9242

Applying the difference of squares identity:

9242=(94)(9+4)

Now we can simplify the terms inside the parentheses:

(94)=5and(9+4)=13

Thus, we have:

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

So the product that equals 8116 is:

513