Question

What is the justification for the first step in proving the formula for factoring the sum of cubes?
A^3+b^3=(a+b)(a^2-ab+b^2)

=a^3a^2b+ab^2+a^2b+ab^2+b^3

A) distributive property
B) commutative property
C) definition of additive inverse
D) definition of mulitiplicative inverse

Answer 1

Answer:

Option A is correct.

Step-by-step explanation:

The formula of $a^{3} + b^{3} = (a+b)(a^{2} -ab+b^{2} )$ can also be written as  

= $a^{3} -a^{2} b+ab^{2} +ba^{2} -ab^{2} +b^{3}$

This is practically an example of distributive property of numbers where we can write as an example  

(a + b ) ( c + d ) = ac + ad + bc + bd  

or,  ( a + b ) ( c − d ) = ac − ad + bc − bd

Therefore, option A is correct. (Answer)