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.
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
Can you finish from here?
That is the answer, but your teacher might not want to see the word "squared" written. I just did that for you for clarity.
Sure! Let's follow these steps to rewrite a two-digit number as a difference of two numbers and square it using the identity (x - y)^2 = x^2 - 2xy + y^2:
1. Choose a two-digit number greater than 25. Let's say we choose the number 37.
2. Rewrite your two-digit number as a difference of two numbers. We can choose any convenient numbers that add up to our chosen two-digit number. For instance, let's use 40 and 3, such that 40 - 3 = 37.
3. Now, we will use the identity (x - y)^2 = x^2 - 2xy + y^2 to square our chosen number without a calculator.
- Start by squaring each number:
- (40)^2 = 1600
- (3)^2 = 9
- Then, multiply twice the product of the two numbers:
- 2 * 40 * 3 = 240
- Finally, add the squared values and twice the product:
- 1600 - 240 + 9 = 1369
So, when we square the number 37 without using a calculator, we get 1369.
Remember that when applying this method to a different two-digit number, you'll need to adjust the numbers you choose in step 2 accordingly to ensure their sum still equals the original two-digit number.
It is kind of difficult for me.
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
so instead of putting 40 squared i would put 40^2 correct? Thank you!
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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.