Answer: 3 23 divided by 22 = 2(3 - 2) = 21 = 2 think it’s 2
Step-by-step explanation: Changes made to your input should not affect the solution:
(1): "^-2" was replaced by "^(-2)".
(2): "y4" was replaced by "y^4".
STEP
1
:
Equation at the end of step 1
(((0-((2x•(y3))•z))-2)3)•(((2x2•y4)•z)-2)
STEP
2
:
Equation at the end of step
2
:
(((0 - (2xy3 • z)) - 2)3) • (2)(-2)x(-4)y(-8)z(-2)
STEP
3
:
STEP
4
:
Pulling out like terms
4.1 Simplify ( -2xy3z-2 )3
Put the exponent aside and simplfy the base by pulling out like factors :
-2xy3z-2 = -2 • (xy3z+1)
Remember the 4th law of exponents : (a • b)m= am• bm
Retract the exponent and apply the 4th law to the simplified base: ( -2 • (xy3z+1) )3 = (-2)3 • (xy3z+1)3
Trying to factor as a Sum of Cubes:
4.2 Factoring: xy3z+1
Put the exponent aside, try to factor xy3z+1
Theory : A sum 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 : 1 is the cube of 1
Check : x 1 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Dividing exponents:
4.3 23 divided by 22 = 2(3 - 2) = 21 = 2
Final result :
-2 • (xy3z + 1)3
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x12y24z6
