Question

(d) 8ax + 12a - 4az
2​

Answer 1

Answer:

Changes made to your input should not affect the solution:

(1): "x1"   was replaced by   "x^1".  

STEP

1

:

Equation at the end of step 1

 (23ax12 • a) -  4az

STEP  

2

:

STEP  

3

:

Pulling out like terms :

3.1     Pull out like factors :

  8a2x12 - 4az  =   4a • (2ax12 - z)  

Trying to factor as a Difference of Squares:

3.2      Factoring:  2ax12 - z  

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 :  2  is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Trying to factor as a Difference of Cubes:

3.3      Factoring:  2ax12 - z  

Theory : A difference of two perfect cubes,  a3 - b3 can be factored into

             (a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =

           a3+a2b+ab2-ba2-b2a-b3 =

           a3+(a2b-ba2)+(ab2-b2a)-b3 =

           a3+0+0+b3 =

           a3+b3

Check :  2  is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Final result :

 4a • (2ax12 - z)