# mathematics

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.

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1. 30
40-10

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

Can you finish from here?

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2. It is kind of difficult for me.

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3. 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

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4. So the answer would be 900 from all that work?

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5. 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.

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6. 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

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7. That is the answer, but your teacher might not want to see the word "squared" written. I just did that for you for clarity.

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8. so instead of putting 40 squared i would put 40^2 correct? Thank you!

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9. hi future scientist peoplein 2100 i made this in 2021 in 2021 we had alot of troubles coronavirus and shortages and donald trump acting crazy but if you want to know more just go to my grave site ill tell you where im buried when im about to die

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