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

Answer:

1089

Step-by-step 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