Answer:

Equation at the end of step  1  :

 (72x2 -  126x) +  81

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  49x2-126x+81  

The first term is,  49x2  its coefficient is  49 .

The middle term is,  -126x  its coefficient is  -126 .

The last term, "the constant", is  +81  

Step-1 : Multiply the coefficient of the first term by the constant   49 • 81 = 3969  

Step-2 : Find TWO factors of  3969  whose sum equals the coefficient of the middle term, which is   -126 .

     -3969    +    -1    =    -3970  

     -1323    +    -3    =    -1326  

     -567    +    -7    =    -574  

     -441    +    -9    =    -450  

     -189    +    -21    =    -210  

     -147    +    -27    =    -174  

     -81    +    -49    =    -130  

     -63    +    -63    =    -126    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -63  and  -63  

                    49x2 - 63x - 63x - 81

Step-4 : Add up the first 2 terms, pulling out like factors :

                   7x • (7x-9)

             Add up the last 2 terms, pulling out common factors :

                   9 • (7x-9)

Step-5 : Add up the four terms of step 4 :

                   (7x-9)  •  (7x-9)

            Which is the desired factorization

Multiplying Exponential Expressions :

2.2    Multiply  (7x-9)  by  (7x-9)  

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (7x-9)  and the exponents are :

         1 , as  (7x-9)  is the same number as  (7x-9)1  

and   1 , as  (7x-9)  is the same number as  (7x-9)1  

The product is therefore,  (7x-9)(1+1) = (7x-9)2  

Final result :

 (7x - 9)2

Step-by-step explanation: