Solution - Power equations

Step  1  :

Equation at the end of step  1  :

  
 Step  2  :

Equation at the end of step  2  :

  
 Step  3  :

Equation at the end of step  3  :

  
 Step  4  :

Equation at the end of step  4  :

Step  5  :

            2a3b2 - 5a2b2 + 10ab2 
 Simplify   —————————————————————
                 -8ab - 3b2      

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   2a³b² - 5a²b² + 10ab²  =   ab² • (2a² - 5a + 10) 

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   -8ab - 3b²  =   -b • (8a + 3b) 

Trying to factor by splitting the middle term

 7.2     Factoring  2a² - 5a + 10 

The first term is,  2a²  its coefficient is  2 .
The middle term is,  -5a  its coefficient is  -5 .
The last term, "the constant", is  +10 

Step-1 : Multiply the coefficient of the first term by the constant   2 • 10 = 20 

Step-2 : Find two factors of  20  whose sum equals the coefficient of the middle term, which is   -5 .

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Dividing exponential expressions :

 7.3    b² divided by b¹ = b^{(2 - 1)} = b¹ = b

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   -8a - 3b  =   -1 • (8a + 3b) 

Final result :

  ab • (2a2 - 5a + 10)
  ————————————————————
        -8a - 3b