Question

4) Factories: 24 a +81b3​

Answer 1

Answer:   3 • (8a + 27b3)

Step-by-step explanation: STEP

1

:

Equation at the end of step 1

 24a +  34b3

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  24a + 81b3  =   3 • (8a + 27b3)  

Trying to factor as a Sum of Cubes:

3.2      Factoring:  8a + 27b3  

Theory : A sum of two perfect cubes,  a3 + b3 can be factored into  :

            (a+b) • (a2-ab+b2)

Proof  : (a+b) • (a2-ab+b2) =

   a3-a2b+ab2+ba2-b2a+b3 =

   a3+(a2b-ba2)+(ab2-b2a)+b3=

   a3+0+0+b3=

   a3+b3

Check :  8  is the cube of  2  

Check :  27  is the cube of   3  

Check :  a 1 is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes