Question

Pick a two digit number greater than 25. Rewrite your two digit number as a difference of two number. Show how to use the identity (x - y)^2 = x^2 -2xy + y^2 to square your number without using a calculator

Answer 1

See explanation

Explanation:

Let our two digit number be 26

Next, we rewrite it as a difference of two numbers

26=32-6

We want to square 26 using the identity:
`(x - y)^2 = x^2 -2xy + y^2`

In this case,

• x=32
• y=6

Substituting into the identity

`(x - y)^2 = x^2 -2xy + y^2\\\\(32-6)^2=32^2-2(32)(6)+6^2\\\\=1024-384+36=676\\\\26^2=676\\\\$Since (32-6)^2=26^2,$ we have shown how to use the identity to square a number.`