Question

Explain why a³- b³ is equal to the sum of the volumes of the sides i, ii, and iii.

b. write an algebraic expression for the volume of each of the three solids. Leave your expressions in factored form.

C. Use the result from part(a) and part (b) to derive the factoring pattern a³- b³​

Answer 1

The cube difference formula states that a³ - b³ can be factored as (a - b)(a² + ab + b²) and the sides i, ii, and iii represent the three terms of the factored expression. The volume of each of the three solids can be expressed as (a - b), (a²), and (b²).

Step-by-step explanation:

In order to understand why a³ - b³ is equal to the sum of the volumes of the sides i, ii, and iii, we need to understand the cube difference formula. The cube difference formula states that a³ - b³ can be factored as (a - b)(a² + ab + b²). In this case, the sides i, ii, and iii represent the three terms of the factored expression: a - b, a², and b².

The algebraic expressions for the volume of each of the three solids can be determined as follows:

The volume of side i is (a - b).

The volume of side ii is (a²).

The volume of side iii is (b²).

Therefore, the factoring pattern for a³ - b³ is (a - b)(a² + ab + b²).