what is the difference between (a + b)^2 and a^2 + b^2?

Answer 1

(a + b)^2 = a^2 + 2ab + b^2

so 2ab is the difference between the 2 expressions.

Now if a and b are both equal to 0, then both expressions would be equal to 0.

Answer 2

Some people do not see the differnece in these two equations because they think that they look the same, and that is an easy and honest mistake. But the difference steams in the fact that in the first equation you are squaring the entire thing within the parenthesis, not each individual term.

In the first one: (a+b)^2 you are squaring the entire opperation inside of the parenthesis, in this case (a+b). You do not square each term by itself, it has to be the entire thing.

A way to see this visually would be to then write it like this:

(a+b)(a+b)

See, its like you are treating the stuff in the equation as one whole. Once you have the equation in this form, you can then multiply out the terms, like this:

(a)(a)= a^2
(a)(b)=ab
(b)(a)=ab
(b)(b)=b^2

Once you add like terms you get the following answer:

a^2+ 2ab+ b^2

In the second one, a^2+b^2, the answer is just that, a^2+b^2. There is nothing that you can simplify or combine like terms. Just square the terms and add.

Like the other answers said, try subsituting actual numbers for the letter variables, like 2 & 3. Doing this will make it easier to understand because you can get a tangible answer without any letter variables. Once you do, you will get two complete different answers.

Hope this helps and was understandable.

Answer 3

Huge difference ie

(2+3)^2 = 25
2^2 + 3^2 =13

Answer 4

(a+b)^2 = a^2 + 2ab + b^2

Try it with a = 1, b = 2
(a+b)^2 = (3)^2 = 9
a^2 + b^2 = 1^2 + 2^2 = 1 + 4 = 5, which is not = 9

Answer 5

IN (a+b)^2 u must first add a+b before squaring the number. IN a^2+b^2, a is squared and b is squared then they are added. ex: a=2 b=5
(a+b)^2=
(2+5)^2
7^2
49

a^2+b^2
2^2+5^2
4+25
29

Answer 6

the main difference between the two are as follows:
(a+b)^2=(a+b)(a+b)
=a(a+b)+b(a+b)
=a^2+ab+ab+b^2
=a^2+2ab+b^2
Where as a^2+b^2 is
a*a+b*b

For example:
suppose a=2 and b=9
(2+9)^2=2^2+2*2*9+9^2
=4+36+81
=121
where as
2^2+9^2
2*2+9*9
=4+81
=85

Answer 7

(a+b)^2 is the sum of a and b squared..
a^2 + b^2 is a squared plus b squared..
For example:
If a is 5 and b is 6,
(a+b)^2 = 121
a^2 + b^2 = 61

Answer 8

2+2=4^2=16 and 2^2+2^2=8, maybe think about it next time, I have drank over a fifth of whiskey and still could answer this one.

Answer 9

(a+b)^2= a^2+ 2ab+ b^2

Answer 10

because in (a+b)^2 you add a and b then square it. In a^2 + b^2 you square and a b first then add them together. Order of Operations