Question

(3a+b/2)2 = (3a)^2 (3a)+(b/2)+b^2​

Answer 1

Answer:

Hiii Hope this helps

Step-by-step explanation:

Step  1  :

           b2

Simplify   ——

           3  

Equation at the end of step  1  :

           b2          

 ((a2) -  (—— • a)) -  3b

           3            

Step  2  :

Rewriting the whole as an Equivalent Fraction :

2.1   Subtracting a fraction from a whole

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

          a2     a2 • 3

    a2 =  ——  =  ——————

          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 :

2.2       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:

a2 • 3 - (ab2)     3a2 - ab2

——————————————  =  —————————

      3                3    

Equation at the end of step  2  :

 (3a2 - ab2)    

 ——————————— -  3b

      3          

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a whole from a fraction

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

         3b     3b • 3

   3b =  ——  =  ——————

         1        3    

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  3a2 - ab2  =   a • (3a - b2)  

Trying to factor as a Difference of Squares :

4.2      Factoring:  3a - b2  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  3  is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Adding fractions that have a common denominator :

4.3       Adding up the two equivalent fractions

a • (3a-b2) - (3b • 3)     3a2 - ab2 - 9b

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

          3                      3        

Trying to factor a multi variable polynomial :

4.4    Factoring    3a2 - ab2 - 9b  

Try to factor this multi-variable trinomial using trial and error  

Factorization fails

Final result :

 3a2 - ab2 - 9b

 ——————————————

       3