S^2+20s+100=
whats the answer

(s - 10)2

Step-by-step explanation:

The first term is,  s2  its coefficient is  1 .

The middle term is,  -20s  its coefficient is  -20 .

The last term, "the constant", is  +100  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 100 = 100  

Step-2 : Find two factors of  100  whose sum equals the coefficient of the middle term, which is   -20 .

     -100    +    -1    =    -101  

     -50    +    -2    =    -52  

     -25    +    -4    =    -29  

     -20    +    -5    =    -25  

     -10    +    -10    =    -20    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  -10  

                    s2 - 10s - 10s - 100

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

                   s • (s-10)

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

                   10 • (s-10)

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

                   (s-10)  •  (s-10)

            Which is the desired factorizationMultiply  (s-10)  by  (s-10)  

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

In our case, the common base is  (s-10)  and the exponents are :

         1 , as  (s-10)  is the same number as  (s-10)1  

and   1 , as  (s-10)  is the same number as  (s-10)1  

The product is therefore,  (s-10)(1+1) = (s-10)2  

Final result :

 (s - 10)2

a. is correct