Question

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

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

Step-by-step explanation:

Answer 2

a^3 b−a^2 b^2−b^3 =b(a^3 −a ^2 b−b^2 )