Question

0.5(8x+4) + (2x+ 1)k(2x+1)​

Answer 1

Try 40x+20+4kxexponet2+4kx+k

Answer 2

Answer:

 (-2x - 1) • (2xk + k - 2)

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

   5

 (——•(8x+4))+(k•(2x+1)•(2x+1))

  10

Step  2  :

Multiplying Exponential Expressions :

2.1    Multiply  (2x+1)  by  (2x+1)  

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

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

         1 , as  (2x+1)  is the same number as  (2x+1)1  

and   1 , as  (2x+1)  is the same number as  (2x+1)1  

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

Equation at the end of step  2  :

   5                

 (—— • (8x + 4)) +  k • (2x + 1)2

  10                

Step  3  :

           1

Simplify   —

           2

Equation at the end of step  3  :

  1                

 (— • (8x + 4)) +  k • (2x + 1)2

  2                

Step  4  :

Step  5  :

Pulling out like terms :

5.1     Pull out like factors :

  8x + 4  =   4 • (2x + 1)  

Equation at the end of step  5  :

 2 • (2x + 1) +  k • (2x + 1)2

Step  6  :

Pulling out like terms :

6.1      Pull out     2x+1  

After pulling out, we are left with :  

     (2x+1) • ( 2  *  1 - k  *  (2x+1) ))

Step  7  :

Pulling out like terms :

7.1     Pull out like factors :

  -2xk - k + 2  =   -1 • (2xk + k - 2)  

Final result :

 (-2x - 1) • (2xk + k - 2)