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

Option A is correct.

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)