Pick 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 = x^2 − 2xy + y^2 to square your number without using a calculator.

The number is 30.

Question

Pick 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 = x^2 − 2xy + y^2 to square your number without using a calculator.

The number is 30.

carmelle · Answer

@AZ can you help?

carmelle · Answer

@darkknight can you help?

carmelle · Answer

@snowflake0531 can u help :)

snowflake0531 · Answer

Well choose 2 numbers _-_ = 30

Florisalreadytaken · Answer

the point of this is to find what the square of that number would be, without using a calculator

ok, so you picked 30

lets rewrite that as a difference of 2 numbers -- so that would be $35-5$

where

$ x=35 $

$ y=5  $

substitute that into this

$(x − y)^2 = x^2 − 2xy + y^2$

Florisalreadytaken · Answer

actually, whats the point of this?😂

Florisalreadytaken · Answer

you would use that calculator to find $  35^2   $ anyway

carmelle · Answer

ok

$$(35 - 5)^{2} = 35^2 - 2(35)(5) + y^2$$

carmelle · Answer

5^2 *

carmelle · Answer

@florisalreadytaken wrote:

you would use that calculator to find $ 35^2 $ anyway

fr smh

carmelle · Answer

1225 - 350 + 25

is this correct?

Florisalreadytaken · Answer

ok, sp by doing the whole thing in 1 go, it will be:

$ (x − y)^2 = x^2 − 2xy + y^2 $

$  (35 - 5)^{2} = 35^2 - 2(35)(5) + 5^2 $

$ 900 =1225 -350 + 25  $

$ 900= 900$

carmelle · Answer

thank you sooo much :D

Florisalreadytaken · Answer

you got it :D

AZ · Answer

@florisalreadytaken wrote:

actually, whats the point of this?😂

@florisalreadytaken wrote:

you would use that calculator to find $ 35^2 $ anyway

Perhaps if you used simpler numbers like 30^2 = (40-10)^2 then you wouldn't have to use a calculator but the purpose of this assignment seems to be just teaching you the identity and not necessarily the most efficient way of finding the square of a number