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.
Answers
John
30
40-10
(40-10)^2 = 40^2 -2(40)(10) + 10^2
Can you finish from here?
40-10
(40-10)^2 = 40^2 -2(40)(10) + 10^2
Can you finish from here?
brandy
It is kind of difficult for me.
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
Now, look at the other side of the equation.
40 squared = 1600
2(40)(10) = 800
10 squared = 100
1600 - 800 + 100 = 900
brandy
So the answer would be 900 from all that work?
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.
(x − y)^2 = x^2 − 2xy + y^2
We showed that 900= 900
It was a lot of work, but proved the equation works.
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
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
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.
Sally
so instead of putting 40 squared i would put 40^2 correct? Thank you!
j
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