(a + b)^2 = a^2 + b^2? Is that not true?

Question

Why?

Answer 1

nope! because it is not equal!
(a+b)^2 is:
(a+b)^2= a^2+2ab+b^2

Answer 2

It is if a=0 or b=0 because:

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

Answer 3

No, it isn't.
example: a=2 b=1
(2+1)^2=3^2=9
2^2+1^2=4+1=5, and 9 is not equal to 5.
(a+b)^2=a^2+2ab+b^2
(a+b)^2=(a+b)(a+b)

Answer 4

That's a very fundamental error. I'm sure somewhere in your text book, there is a highlighted note that clearly says
(a+b)^2 is NOT equal to a^2 + b^2

If it helps try plugging in two values for a and b.
Say a = 1, b = 2.
(a+b)^2 = 3^2 = 9
a^2 + b^2 = 1^2 + 2^2 = 1 + 4 = 5
So you see they are not equal.

Answer 5

Megha is correct.

(a + b)(a +b)
Then FOIL IT
a^2 + ab + ab +b^2
a^2 + 2ab + b^2

Answer 6

No
(a+b)(a+b)
= a(a+b)+b(a+b)
=a.a+a.b+b+.a+b.b
=a^2+b^2+2ab

Answer 7

it is not true

simple F.O.I.L.

First, outside, inside, last

write it out...

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

= a^2 +ab+ab+b^2
F =a^2
O = ab
I = ab
L = b^2
simplified = a^2+2ab+b^2

Answer 8

(a + b)(a + b)
a² + ab + ba + b²
a² + 2ab + b²