Which expression equivalent to 9q^ 2 - 2 3 (3q-7)+5q^ 2 ? A 9q ^ 2 - 5/3 * q - 3 B 9q ^ 2 - 2q - 3 14q ^ 2 - 2q + 14/3 D 14q ^ 2 - 5/3 * q - 14/3 D

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "q2"   was replaced by   "q^2".  1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

            2

 ((9•(q2))-(—•(3q-7)))+5q2

            3

STEP

2

:

           2

Simplify   —

           3

Equation at the end of step

2

:

                 2                  

 ((9 • (q2)) -  (— • (3q - 7))) +  5q2

                 3                  

STEP

3

:

Equation at the end of step 3

                2 • (3q - 7)      

 ((9 • (q2)) -  ————————————) +  5q2

                     3            

STEP  

4

:

Equation at the end of step

4

:

          2 • (3q - 7)      

 (32q2 -  ————————————) +  5q2

               3            

STEP

5

:

Rewriting the whole as an Equivalent Fraction

5.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  3  as the denominator :

            32q2     32q2 • 3

    32q2 =  ————  =  ————————

             1          3    

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

5.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

32q2 • 3 - (2 • (3q-7))     27q2 - 6q + 14

———————————————————————  =  ——————————————

           3                      3        

Equation at the end of step

5

:

 (27q2 - 6q + 14)    

 ———————————————— +  5q2

        3            

STEP

6

:

Rewriting the whole as an Equivalent Fraction :

6.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  3  as the denominator :

          5q2     5q2 • 3

   5q2 =  ———  =  ———————

           1         3    

Trying to factor by splitting the middle term

6.2     Factoring  27q2 - 6q + 14  

The first term is,  27q2  its coefficient is  27 .

The middle term is,  -6q  its coefficient is  -6 .

The last term, "the constant", is  +14  

Step-1 : Multiply the coefficient of the first term by the constant   27 • 14 = 378  

Step-2 : Find two factors of  378  whose sum equals the coefficient of the middle term, which is   -6 .

     -378    +    -1    =    -379  

     -189    +    -2    =    -191  

     -126    +    -3    =    -129  

     -63    +    -6    =    -69  

     -54    +    -7    =    -61  

     -42    +    -9    =    -51  

For tidiness, printing of 26 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Adding fractions that have a common denominator :

6.3       Adding up the two equivalent fractions

(27q2-6q+14) + 5q2 • 3     42q2 - 6q + 14

——————————————————————  =  ——————————————

          3                      3        

STEP

7

:

Pulling out like terms :

7.1     Pull out like factors :

  42q2 - 6q + 14  =   2 • (21q2 - 3q + 7)  

Trying to factor by splitting the middle term

7.2     Factoring  21q2 - 3q + 7  

The first term is,  21q2  its coefficient is  21 .

The middle term is,  -3q  its coefficient is  -3 .

The last term, "the constant", is  +7  

Step-1 : Multiply the coefficient of the first term by the constant   21 • 7 = 147  

Step-2 : Find two factors of  147  whose sum equals the coefficient of the middle term, which is   -3 .

     -147    +    -1    =    -148  

     -49    +    -3    =    -52  

     -21    +    -7    =    -28  

     -7    +    -21    =    -28  

     -3    +    -49    =    -52  

     -1    +    -147    =    -148  

     1    +    147    =    148  

     3    +    49    =    52  

     7    +    21    =    28  

     21    +    7    =    28  

     49    +    3    =    52  

     147    +    1    =    148  

Observation : No two such factors can be found !!

Conclusion : Trinomial cannot be factored

Final result :

 2 • (21q2 - 3q + 7)

 ———————————————————

          3