Question

Given: 4 < a < 5, 2 < b < 4

Answer 1

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 ab • (a + b) • (a - b)

Step-by-step explanation:

a3b-b3a  

Step by step solution :

Step  1  :

Step  2  :

Pulling out like terms :

2.1     Pull out like factors :

  a3b - ab3  =   ab • (a2 - b2)  

Trying to factor as a Difference of Squares :

2.2      Factoring:  a2 - b2  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  a2  is the square of  a1  

Check :  b2  is the square of  b1  

Factorization is :       (a + b)  •  (a - b)  

Final result :

 ab • (a + b) • (a - b)