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
Step 1: Distributive Property
Step 2: Combine like terms
Step 3: Combine like terms
Step 4: Commutative Property of Addition
Step 1: Distributive Property
Step 2: Combine like terms
Step 3: Combine like terms
Step 4: Commutative Property of Addition
Step 1: Distributive Property - This step is using the distributive property to expand (a+b)^3 and simplify the terms.
Step 2: Combine like terms - This step is combining like terms by adding -3a^2b and 3a^2b, which cancel each other out.
Step 3: Combine like terms - This step is combining like terms by adding -3ab^2 and 3ab^2, which cancel each other out.
Step 4: Commutative Property of Addition - This step is rearranging the terms to show that a^3 + b^3 = b^3 + a^3.
(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