Hello. Can you please help me solve the below problem? I know it's not irreducible but I don't know how to factor it.

Question

Factor the polynomial or expression. (If a polynomial is irreducible, enter IRREDUCIBLE.)

(a + b)^3 − 8c^3

Answer 1

Paul,

 

Difference of Cubes formula:

 

a^3 - b^3 = (a + b) ( a^2 + ab + b^2)

 

In your problem:

 

(a + b) = a in the formula

 

2c = b in the formula

 

Then in your problem you have:

 

(a + b)^3 - (2c)^3  Difference of two cubes

 

Then you have:

 

(a + b - 2c) [(a + b)^2 + (a + b)(2c) + (2c)^2]

 

 

Answer 2

This is an example of the Difference of Cubes. Look up the rule in your textbook.

 

(a + b)³ - 8c³

(a + b)³ - (2c)³

 

Now using the rule that you have located, factor the last line.