Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  -3ab • (((7 • (a2)) • b) -  5ab3)
 Step  2  :

Equation at the end of step  2  :

  -3ab • ((7a2 • b) -  5ab3)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   7a²b - 5ab³  =   ab • (7a - 5b²) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  7a - 5b² 

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 :  7  is not a square !!

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

Multiplying exponential expressions :

 4.3    a¹ multiplied by a¹ = a^{(1 + 1)} = a²

Multiplying exponential expressions :

 4.4    b¹ multiplied by b¹ = b^{(1 + 1)} = b²

Final result :

  -3a2b2 • (7a - 5b2)