Question 423854
"Explain in your own words why (a+b)^2 is not equal to a^2 + b^2? 
What does (a+b)^2 and (a-b)^2 equal?"


You are squaring two different binomials.
When you square a binomial, you multiply it by itself.


(a + b)^2 
= (a + b)(a + b)
= a(a) + a(b) + b(a) + b(b) {used foil method}
= a^2 + ab + ab + b^2 {multiplied through}
= a^2 + 2ab +  b^2 {combined like terms}


(a - b)^2 
= (a - b)(a - b)
= a(a) + a(-b) - b(a) - b(-b) {used foil method}
= a^2 - ab - ab + b^2 {multiplied through}
= a^2 - 2ab + b^2 {combined like terms}
<a href = "http://www.algebrahouse.com/" target = "_blank">www.algebrahouse.com</a>