SOLUTION: "the difference between the sum of two numbers squared and their sum squared"

Algebra ->  Human-and-algebraic-language -> SOLUTION: "the difference between the sum of two numbers squared and their sum squared"      Log On


   



Question 17562: "the difference between the sum of two numbers squared and their sum squared"
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
The "sum of two numbers squared" is really ambiguous. By this do you mean (and let me add parentheses for emphasis in the wording): "the sum of (two numbers squared)" or "the (sum of two numbers) squared". Do you see the confusion of saying "the sum of two numbers squared" without explaining what you really mean?

The other expression that you gave "their sum squared" is perfectly clear. This means if x and y are the two numbers, then you take the sum of the numbers (x+y) and square it. This means %28x%2By%29%5E2.

Back to the first expression, when you said "the sum of two numbers squared" you probably meant the sum of the squares of two numbers." That would have been much more clear. The sum of the squares of the two numbers x and y, would be x%5E2+%2B+y%5E2.

These are NOT the same, since %28x%2By%29%5E2 actually means x%5E2+%2B+2xy%2By%5E2.

It's even easier to see with numbers. Suppose the numbers are 3 and 4. Then the sum of the squares of the two numbers means 3%5E2+%2B4%5E2+=+9%2B16=25. However, the sum squared means that you take the sum first which would be 7, and squaring that you get 49!

R^2 at SCC