Question

Factorise : a^3b - a^2b^2 - b^3​​​​​​​

Answer 1

 solution :

Step  1  :

Equation at the end of step  1  :

(((a3) • b) - (2a2 • b2)) + ab3

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   a3b - 2a2b2 + ab3  =   ab • (a2 - 2ab + b2) 

Trying to factor a multi variable polynomial :

 3.2    Factoring    a2 - 2ab + b2 

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

 Found a factorization  :  (a - b)•(a - b)

Detecting a perfect square :

 3.3    a2  -2ab  +b2  is a perfect square 

 It factors into  (a-b)•(a-b)
which is another way of writing  (a-b)2

How to recognize a perfect square trinomial:  

 • It has three terms  

 • Two of its terms are perfect squares themselves  

 • The remaining term is twice the product of the square roots of the other two terms

Final result :

ab • (a - b)2

Answer 2

Answer:

b(a^3-a^2b-b^2)

Step-by-step explanation:

a^3b-a^2b^2-b^3

the common is b so

b we will take as common and divide it by each term

b(a^3-a^2b-b^2)