Prove that (a+b)^2 is not the same as a^2 + b^2

Question

Prove:

Prove that

(a+b)^2 is not the same as a^2 + b^2

Answer 1

An easy way of proving that (a+b)^2 is not the same as a^2 + b^2 is to expand the expressions.

Expansion of (a+b)^2

1. (a+b)(a+b)
2. a^2 + ab + ab + b^2
3. a^2 + 2ab + b^2

Expansion of a^2 + b^2

1. a*a + b*b

As you can see these expressions look nothing alike in their expanded or simplified form, therefore the expressions are not the same

Answer 2

if you expand (a + b)^2, you will get a^2 + 2ab + b^2 so the addition of 2ab proves that (a + b)^2 Does Not Equal a^2 + B^2