Why does (x + y)^2(squared) not equal x^2 + y^2?

Question

(^2) means squared. For example, 3^2 = 3 times 3 = 9. Specific examples can be used. I just don't understand why it doesn't work.

Answer 1

The first term means that you are squaring the sum of two numbers. The second term means that you are adding the squares of two numbers. It's rather simple and that's why the parentheses are used, to keep you from misunderstanding. Just plug in a few values for x and y, keeping the same values for your second term each time, and then it'll become clear.

Answer 2

Because the () make the x + y 1 term so u must add them together first before u can square it
(4 + 5) ^2 = 4 + 5 = 9 and 9 ^2 = 81
NOT
4 ^2 + 5 ^2
16 + 25 =
41

Answer 3

The parentheses tell you what to do first. So you add x and y together and then square the result.

Correct:
(2 + 3)^2 = 5^2 = 25

Incorrect
(2 + 3)^2 = 2^2 + 3^2 = 4 + 9 = 13

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Answer 4

If you are squaring (x+y), you will want to multiply (x+y)(x+y). This requires the FOIL method, or another technique for polynomial expansion, and when you do this...
Multiplying the First terms gives x * x or x^2
Multiplying the Outer terms gives x*y
Multiplying the Inner terms gives x*y
Multiplying the Last terms gives y*y or y^2.
If we sum all these up, we end up with x^2 + 2xy + y^2.

You could also try using numbers to prove the statement. For example, (2 + 3)^2 will give us 5^2 or 25, whereas 2^2 + 3^3 gives 4+9 which is only 13.

Answer 5

Since i know that 1+2 = 3
By your reasoning
(1+2)^2 = 1^2 + 2^2 = 1+4 = 5 which does not equal 9!!!
But you already know that 3^2 = 9

You said that 3^2 = 3 times 3 = 3*3 = 9
What do you mean when you say "times"
Multiplication is defined as Repeated Addition
so times means that you are addin 3 three times

Similary (1+2)^2 = (1+2)times (1+2) = (1+2)*(1+2)

Hope this helps

Answer 6

(X+Y)^2 means quantity squared, i.e., if X=2 and Y=5 you get (2+5)^2 or (7)^2 = 49. The other example says that 2^2+5^2 is 4 + 25 which is 29. OK?

Answer 7

it doesn't work because (x+y)^2 is a factored form of x^2+2xy+y^2. 3^2 =9 but it is not the same as (3+2)^2 the rule is you have to sum up the things in the parenthesis first before you apply the ^2. If you want it to work that way take away the parenthesis. The parenthesis changes the way you solve for it.

Answer 8

There are two ways to see why (x+y)^2 /=x^2+y^2.

First: Figure it out algebraically. Write out (x+y)^2 term by term: (x+y)^2=(x+y)(x+y) then multiply this out (x+y)(x+y)=xx+xy+yx+yy=x^2 + 2xy + y^2 and this is not equal to just x^2 + y^2.

Second: Figure it out with geometry. (x+y)^2 equals the area of a square with sides of length (x+y). Draw this square on a piece of paper, and mark each side into two segments of length x and y. For instance, if x=2 inches and y=3 inches, draw a square with sides 5 inches long, and divide each side into two segments 2 and 3 innches long. Now, cut the square into four smaller areas by drawing two straight lines across the square, two inches from two of the sides, so the lines cross. Draw these lines so they are parallel to the square's sides. You now have the larger square cut into four smaller areas: two rectangles each of area xy, plus a square of area xx and another square of area yy. The sum of the smaller areas equals the area of the original square. You get the same formula as in the first paragraph above.

Answer 9

just substitute in a test number

(2 + 6)^2 != 2^2 + 6^2
8^2 != 4 + 36
64 != 40

or just do the simplify the first part and you'll see:
(x + y)^2
x^2 + 2xy + y^2 which doesn't equal the second part.

Answer 10

You are assuming you distribute the "^2" into the binomial like with
2(x + y) which is (2x + 2y).

But, (x + y)^2 means you write (x + y)(x + y), not (x^2 + y^2)
So now you can "distribute" the first (x + y) into the second (x + y)

(x + y)[x + y] = [(x + y)x + (x + y)y]
= [(x*x + y*x) + (x*y + y*y)]
=[(x^2 + yx + xy + y^2)]
=(x^2 + 2xy + y^2)