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

Question 17562: "the difference between the sum of two numbers squared and their sum squared"
Answer by rapaljer(4671) (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 .

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 .

These are NOT the same, since actually means .

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 . 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
RELATED QUESTIONS
The sum of two numbers is 8 and the difference between their squares is 34. Find their... (answered by rakhileshnaidu,Alan3354)

The difference between two numbers is 40 and their sum is 96. Find the two... (answered by solver91311,checkley77)

The sum of two numbers is 19 and their... (answered by josgarithmetic)

The difference between two numbers is 2, and the sum of their squares is 52. Find the... (answered by jorel555)

the difference of 2 numbers is 3.If the difference of their squared is 15,what is the sum (answered by josgarithmetic,ikleyn)

The difference between two numbers is 14 and half of their sum is 25. What are the... (answered by solver91311)

The difference between two numbers is 8 and twice the sum of their reciprocals are equal... (answered by amarjeeth123)

The difference between two numbers is 8 and twice the sum of their reciprocols is equal... (answered by ankor@dixie-net.com)

the difference between two numbers is 21 and their sum is 185.find the largest... (answered by haileytucki)