Asked by brandy

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.
Answered by John
30
40-10

(40-10)^2 = 40^2 -2(40)(10) + 10^2

Can you finish from here?
Answered by brandy
It is kind of difficult for me.
Answered by John
30 squared = 900

Now, look at the other side of the equation.

40 squared = 1600
2(40)(10) = 800
10 squared = 100

1600 - 800 + 100 = 900
Answered by brandy
So the answer would be 900 from all that work?
Answered by John
Your teacher wants you to check that
(x − y)^2 = x^2 − 2xy + y^2

We showed that 900= 900
It was a lot of work, but proved the equation works.
Answered by brandy
so this would be my answer:

30
40-10

(40-10)^2 = 40^2 -2(40)(10) + 10^2

30 squared = 900

40 squared = 1600
2(40)(10) = 800
10 squared = 100

1600 - 800 + 100 = 900

900=900
Answered by John
That is the answer, but your teacher might not want to see the word "squared" written. I just did that for you for clarity.
Answered by Sally
so instead of putting 40 squared i would put 40^2 correct? Thank you!
Answered by j
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