Respuesta :
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)
