Question

Can someone please help me?

It's asking to explain the difference between a^2 + b^2 versus (a+b)^2. I thought they had the same meaning but I guess they don't? If you could just explain how they are different that would be great, but if you want to go above and beyond you could try to do the two methods they provide for explaining too. Thank you so much :)

Answer 1

Explain the difference between
`a^(2) +b^(2)` versus
`(a+b)^(2)`:

The first squares the numbers before adding. The second adds the two numbers before squaring.

One way to test this, lets make a = 2 and b = 3

`a^(2) +b^(2)`

`2^(2) +3^(2)`

= (2 * 2) + (3 * 3)

4 + 9

= 11

`(a+b)^(2) \\(2+3)^(2) \\= (2+3)(2+3)\\ =5 * 5`

= 25

And we know that 11 ≠ 25.

Answer 2

See below

Explanation:

(a+b)2 = a^2 + 2ab + b^2 does not equal a^2 + b^2

Why the 2 ab?

(a+b) ^2 = (a+b)(a+b) <====expand this:

= a^2 + ab + ab + b^2 = a^2 + 2ab + b^2