Question

HELP ASAP!!!

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.

(number chosen) [33]

Answer 1

1089

Explanation:

Consider 33. It can be rewritten as 40-7. First square it

`(40 - 7) ^(2)`

Considering
`(x-y)^2=x^2-2xy+y^2` . We can assign that...

• 
  `x \implies 40`
• 
  `y \implies 7`

Utilizing the formula yields

`{(40 - 7)}^(2) = 40 ^(2) - 2 \cdot 40 \cdot 7 + {7}^(2)`

simplify....

`{(40 - 7)}^(2) = 40 ^(2) - 2 \cdot 40 \cdot 7 + {7}^(2) \\ \implies {(40 - 7)}^(2) = 1600 - 560 + 49 \\ \implies {(40 - 7)}^(2) = 1649 - 560 \\ \implies {(40 - 7)}^(2) = \boxed{1089}`

Hence, 33²=1089

Recommended book for you: The art of problem solving: introduction to basic algebra by Richard Rusczyk