Question

Topic: Polynomial IdentitiesPick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)2 = x2 − 2xy + y2 to square your number without using a calculator.

Answer 1

Rewriting 28 as a difference of two numbers, we have:

$28=30-2$

Then, applying our identity:

$28^2=(30-2)^2=30^2-2(30)(2)+2^2=900-120+4=784$