if (ab)^2 =a^2 b^2 , does (a+b)^2= a^2+b^2 ? Why or why not?

Question

if (ab)^2 =a^2 b^2 , does (a+b)^2= a^2+b^2 ? Why or why not?

Answer 1

(AB)^2 = A^2*B^2

(A+B)^2 = (A+B)(A+B) In order to solve this multiplication problem we need to use FOIL

 

FOIL stands for:

1. First - Multiply the first terms in each expression: A*A = A^2
2. Outer - Multiply the outer terms in each expression: A*B = AB
3. Inner - Multiply the inner terms in each expression: B*A = AB
4. Last - Multiply the last terms in each expression: B*B=B^2

When we put these into one equation we get the following:

A^2+AB+AB+B^2

This reduces down to: A^2 + 2AB + B^2