12vx^2y^8–28v^4x^9 What is the answer

Question

12vx^2y^8–28v^4x^9
What is the answer

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Gianna 5 months 2021-12-27T12:11:22+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-12-27T12:12:47+00:00

    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)

    0
    2021-12-27T12:13:16+00:00

    48vx^x(16y^2-21v) a lot of steps but you got this

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