12vx^2y^8–28v^4x^9
What is the answer

 6vx2 • (3v4x6 - 2y6)

Step-by-step explanation:

18v5x8-12vx2y6  

Final result :

 6vx2 • (3v4x6 - 2y6)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((18•(v5))•(x8))-((22•3vx2)•y6)

Step  2  :

Equation at the end of step  2  :

 ((2•32v5) • x8) -  (22•3vx2y6)

Step  3  :

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  18v5x8 - 12vx2y6  =   6vx2 • (3v4x6 - 2y6)  

Trying to factor as a Difference of Squares :

4.2      Factoring:  3v4x6 - 2y6  

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

Trying to factor as a Difference of Cubes:

4.3      Factoring:  3v4x6 - 2y6  

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 :  3  is not a cube !!

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

Final result :

 6vx2 • (3v4x6 - 2y6)18v5x8-12vx2y6  

Final result :

 6vx2 • (3v4x6 - 2y6)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((18•(v5))•(x8))-((22•3vx2)•y6)

Step  2  :

Equation at the end of step  2  :

 ((2•32v5) • x8) -  (22•3vx2y6)

Step  3  :

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  18v5x8 - 12vx2y6  =   6vx2 • (3v4x6 - 2y6)  

Trying to factor as a Difference of Squares :

4.2      Factoring:  3v4x6 - 2y6  

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

Trying to factor as a Difference of Cubes:

4.3      Factoring:  3v4x6 - 2y6  

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 :  3  is not a cube !!

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

Final result :

 6vx2 • (3v4x6 - 2y6)

2/5

step-by-step explanation:

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