Question

12vx^2y^8–28v^4x^9
What is the answer

Answer 1

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

Answer 2

6vx2 • (3v4x6 - 2y6)

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)