Question

Read the following proof of the polynomial identity a3+b3=(a+b)3−3ab(a+b).

Step 1: a3+b3=a3+3a2b+3ab2+b3−3ab(a+b)
Step 2: a3+b3=a3+3a2b+3ab2+b3−3a2b−3ab2
Step 3: a3+b3=a3+3a2b−3a2b+3ab2−3ab2+b3
Step 4: a3+b3=a3+b3

Match each step with the correct reason.

Commutative Property of Addition
Binomial Theorem
Distributive Property
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Combine like terms

Answer 1

(a+b)^3 = a^3 + 3a^2 b + 3a b^2 + b^3
(a+b)^3 = a^3 + b^3 + 3ab(a+b)
re-arranging:
a^3 + b^3 = (a+b)^3 - 3ab(a+b)

don't know what all that other stuff is supposed to be