2120.11 – Messy Numerical Expression

Find the value of the expression, ${1379^2}-(2)(1379)(379)+{379^2},$ without using a calculator. Also without doing a lot of work.

Hint: Use 'algebra eyes' to 'see' that the given expression fits a common algebraic formula.

Solution

The given expression is in the form:

${x^2} - 2xy + {y^2} = {(x-y)^2},$

with $x = 1379$ and $y = 379$ . Then $x - y = 1000$ and so

${1379^2}-(2)(1379)(379)+{379^2} = {1000^2} = 1,000,000.$

Voila.