Question

Solve the equation 6C21-D82A=28B2

Answer 1

2⋅(2b−1)⋅(7b+3(ANS)

2⋅(2b−1)⋅(7b+3

See steps

Step by Step Solution:

(1): "b2"   was replaced by   "b^2".

STEP

1

:

Equation at the end of step 1

 ((22•7b2) -  2b) -  6

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  28b2 - 2b - 6  =   2 • (14b2 - b - 3)

Trying to factor by splitting the middle term

3.2     Factoring  14b2 - b - 3

The first term is,  14b2  its coefficient is  14 .

The middle term is,  -b  its coefficient is  -1 .

The last term, "the constant", is  -3

Step-1 : Multiply the coefficient of the first term by the constant   14 • -3 = -42

Step-2 : Find two factors of  -42  whose sum equals the coefficient of the middle term, which is   -1 .

     -42    +    1    =    -41

     -21    +    2    =    -19

     -14    +    3    =    -11

     -7    +    6    =    -1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  6

                    14b2 - 7b + 6b - 3

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

                   7b • (2b-1)

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

                   3 • (2b-1)

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

                   (7b+3)  •  (2b-1)

            Which is the desired factorization

Final result :

 2 • (2b - 1) • (7b + 3