Question

12vx^2y^8–28v^4x^9

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3 weeks 2021-12-27T12:11:22+00:00 2 Answers 0 views 0

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