Question

the factors of 4s²-4s_1​

Answer 1

Answer:

(1): "s2"   was replaced by   "s^2". 

STEP1:Equation at the end of step 1

(22s2 - 4s) + 1

STEP2:Trying to factor by splitting the middle term

 2.1     Factoring  4s2-4s+1 

The first term is,  4s2  its coefficient is  4 .

The middle term is,  -4s  its coefficient is  -4 .

The last term, "the constant", is  +1 

Step-1 : Multiply the coefficient of the first term by the constant   4 • 1 = 4 

Step-2 : Find two factors of  4  whose sum equals the coefficient of the middle term, which is   -4 .

     -4   +   -1   =   -5     -2   +   -2   =   -4   That's it

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

                     4s2 - 2s - 2s - 1

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

                    2s • (2s-1)

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

                     1 • (2s-1)

example:

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

In our case, the common base is  (2s-1)  and the exponents are :

          1 , as  (2s-1)  is the same number as  (2s-1)1 

 and   1 , as  (2s-1)  is the same number as  (2s-1)1 

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

Final result :

(2s - 1)2

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