Question

How did you completely factor the sum and difference of two cubes? Write the process
of each and their rule or pattern.
There are cases in which the​

Answer 1

Step-by-step explanation:

For the difference of cubes, the "minus" sign goes in the linear factor, a – b; for the sum of cubes, the "minus" sign goes in the quadratic factor, a2 – ab + b2. ... When you're given a pair of cubes to factor, carefully apply the appropriate rule.

Answer 2

Answer:

Shown below is the method how we can completely factorize the sum or difference of two cubes.

Step-by-step explanation:

The complete factorization of the sum or difference of two cubes is done by using a simple formula.

Let a³ and b³ be two cubes.

Sum of the two cubes = (a³+b³)

Difference of two cubes = (a³-b³)

1. For factorizing the sum of two cubes -

   (a³+b³) = (a+b)(a²-ab+b²)

For example - Factor the expression (a³+27)

∴ According to the formula (a³+27) = (a)³ + (3)³ = (a+3)(a²-3a+3²)

                                                          = (a+3)(a²-3a+9)

2. For factorizing the difference of two cubes -

   (a³-b³) = (a-b)(a²+ab+b²)

For example - Factor the expression (a³-27)

∴ According to the formula (a³+27) = (a)³ - (3)³ = (a-3)(a²+3a+3²)

                                                          = (a-3)(a²+3a+9)

This is the method how we can completely factorize the sum or difference of two cubes.