Question

3a^7b-24a^4b^4 factorise this..

Answer 1

3a⁷b-24a⁴b⁴=3a⁴b(a³-8b)

Answer 2

Answer:3a4b • (a - 2b) • (a2 + 2ab + 4b2)

Step-by-step explanation:STEP  1  :

Equation at the end of step 1

 ((3 • (a7)) • b) -  ((23•3a4) • b4)

STEP  2  :

Equation at the end of step  2

:

 (3a7 • b) -  (23•3a4b4)

STEP  3  :

STEP  4 :

Pulling out like terms

4.1     Pull out like factors :

  3a7b - 24a4b4  =   3a4b • (a3 - 8b3)  

Trying to factor as a Difference of Cubes:

4.2      Factoring:  a3 - 8b3  

Theory : A difference 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 :  a3 is the cube of   a1

Check :  b3 is the cube of   b1

Factorization is :

            (a - 2b)  •  (a2 + 2ab + 4b2)  

Trying to factor a multi variable polynomial :

   Factoring    a2 + 2ab + 4b2  

Try to factor this multi-variable trinomial using trial and error  

Factorization fails

Final result :

 3a4b • (a - 2b) • (a2 + 2ab + 4b2)

HOPE IT HELPS YOU MATE!