Factorize x^6 – 64.

We could write 64 as a power of
2:

64 = 2^6

Now, we can apply the
formula:

x^n - a^n = (x-a)(x^(n-1) + x^(n-2)*a + .... +
a^(n-1))

We'll put n = 6 and a =
2:

x^6 - 2^6 = (x-2)(x^5 + 2x^4 + 4x^3 + 8x^2 + 16x +
32)

We also could
write:

(x^2)^3 - (2^2)^3

a^3 - b^3 =
(a-b)(a^2 + ab + b^2)

We'll put a = x^2 and b =
2^2

(x^2)^3 - (2^2)^3 = (x^2 - 4)(x^4 + 4x^2 +
16)

But x^2 - 4 is a difference of
squares:

x^2 - 4 = (x-2)(x+2)

(x^2)^3 -
(2^2)^3 = (x-2)(x+2)(x^4 + 4x^2 + 16)

x^6 - 2^6 =
(x-2)(x+2)(x^4 + 4x^2 + 16)

How does the author lead the reader to the "twist ending" in "The Lottery"?

Jackson's use of foreshadowing is powerful and well-played in
The Lottery.  Yes, as discussed above, the beautiful day and the seemingly innocent gathering of
stones by the boys (notice that it's the boys who gather stones - something we'd associate with
boys, not girls), and the general harmonious mood of everyone, definitely lead us to believe that
something wonderful is about to occur.  Further, Tessie Hutchinson's arrival and her seemingly
scatterbrained attitude, mingled with excitement, further mislead the reader.  However, Jackson
also gives us other clues - the predominance of black (the box, the black spot on the paper, even
the names of certain people), not to mention the general air of nervousness and discomfort among
the villagers as the story progresses all serve as
foreshadowing.

One of the most disturbing aspects is that at the end
of the story, when the reader begins to realize that something is VERY wrong, someone hands
little Davy Hutchinson some pebbles - the thought of a 4/5 yr. old child throwing stones at his
mother is anathema to us as readers.  Yet Jackson presents us with this line as a further
foreshadowing of the horror to come, as well as a comment on how no one is
exempt.

(8x^3-27)/(4x^2-9)

To evaluate the expression we'll use factorization. We
notice that the numerator is a difference of cubes:

8x^3-27
= (2x)^3 - (3)^3

We'll apply the
formula:

a^3 - b^3 = (a-b)(a^2 + ab +
b^2)

We'll put a = 2x and b =
3

(2x)^3 - (3)^3 = (2x-3)(4x^2 + 6x +
9)

We also notice that the denominator is a difference of
squares:

4x^2-9 = (2x)^2 -
3^2

We'll apply the
formula:

a^2 - b^2 =
(a-b)(a+b)

(2x)^2 - 3^2 =
(2x-3)(2x+3)

We'll substitute the differences by their
products:

 [(8x^3-27)/(4x^2-9)] = (2x-3)(4x^2 + 6x +
9)/(2x-3)(2x+3)]

We'll simplify by the common factor
(2x-3):

 [(8x^3-27)/(4x^2-9)] =  [(4x^2 + 6x
+ 9)/(2x+3)]

We can also combine the terms
6x + 9 and factorize them by 3;

[(8x^3-27)/(4x^2-9)] =
4x^2/(2x+3) + (6x + 9)/(2x+3)

[(8x^3-27)/(4x^2-9)] =
4x^2/(2x+3) + 3(2x + 3)/(2x+3)

We'll simplify the last
ratio by (2x+3) and we'll
get:

[(8x^3-27)/(4x^2-9)] = [4x^2/(2x+3)] +
3

What does London representin William Blake's "London"?

Blake's poem "London" is the antithesis of his earlier
poems in "Songs of Innocence."  In the earlier poems, innocent children frolic,nature is
in bloom, and people are happy and loving.  It is a time parallel to the time before the
Fall.  But, in "London" which Blake chooses to attack
specifically the corruption in England's government and church, there is no allusion to
a natural world except the Thames River, which, unnaturally, has been "charter'd"; that
is, owned and bound by British law.

Thus,
London represents the evils of English society as the capital of England
and the center of its culture.  The strength of Blake's poem lies in its
ironic contrasts.  The chimney sweep's cry is an affront to the Christianity that the
Church of England promulgates and the soldier who fights to preserve the monarchy sheds
his blood for only the palace walls:

readability="11">

How the chimney sweeper's
cry

Every blackening church
appals

And the hapless soldier's
sigh

Runs in blood down palace
walls.

Blake also decries the
institutions of English rule, centered in London.  He writes
that

In every
voice, in every ban

The mind-forged manacles I
hear.

With ironic use of
"ban" for marriage that binds together people who do not love one another, Blake reviles
the one sacrament that should offer hope: marriage.  But the unhappy husband goes to the
harlot, who in turn gives him syphlis that he passes on to his wife, causing "the
new-born infant's tear" as it is blinded.

By walking
specifically through the streets of London, the capital city of England, Blake uses
imagery and irony to point to the egregious conditions of his English government and
church.

What does Benvolio mean when he says, "We'll measure them a measure and be gone" in Act 1 of Romeo and Juliet?

This line occurs in Act I, scene iv as Mercutio, Benvolio and
Romeo are preparing to go, uninvited, to Capulet's feast.  The have, as was a custom of the day,
entered masked, and are preparing to show up for free food, drink, and dancing with the ladies at
their table of the Capulets.

The line you quote appears in context
like this:

We'll have
no Cupid hoodwink'd with a scarf,

Bearing a Tartar's painted bow of
lath,

Scaring the ladies like a
crowkeeper,

Nor no without-book prologue, faintly
spoke

After the prompter, for our
entrance.

But let them measure us by what they
will,

We'll measure them a measure and be
gone.

What Benvolio is doing in the
first part of this speech is commenting on how there won't be a great to-do over their entrance,
no pomp and circumstance, because they are, in effect, uninvited
guests.

In the final two lines, he's playing with the different
meanings of the word "measure."  In paraphrase, Benvolio says, "Let them judge us ("measure us")
however they want, but we're going to give them (""measure them") a dance ("measure") and then
leave."

For more on this scene, please follow the links
below.

Describe the fall of Enron, according to Drucker's beliefs of an organization in a Post-Capitalist Society?Peter Druckers terms and definitions...

There are some basic elements of Drucker's thoughts that
Enron and "the smartest guys in the room" violated.  I would strongly suggest watching
the film "Enron:  The Smartest Guys in the Room" or reading the book by the same name. 
I think that the most basic element of Drucker's theory which was violated was the
notion of community.  When we hear of CEO Skilling misreading Dawkins' work as a
justification for greed at all costs and the idea of summarily firing the bottom 15% of
employees based on performance evaluations, one is reminded of Drucker's idea that there
has to be a sense of community in business endeavors.  The drive to provide for
employees' social needs and sense of belonging was fairly violated by Enron.  At the
same time, Enron did not see itself as needing to respect the worker or the consumer, as
it bankrolled its own coffers at the cost of both.  When we hear Enron traders mock
about "stealing grandma's savings," one is quickly reminded of
this.

Analyze Hamlet in Shakespeare's play, Hamlet, from psychoanalytic point of view.

One might expect a psychoanalytic study of Hamlet in
Shakespeare's play by the same name might deal with his mental and emotional
issues.

Hamlet learns that his father has been murdered at his Uncle
Claudius' hand, and Hamlet announces his intent to pretend madness to gather evidence. We also
know that Hamlet is plagued by indecision, which is very much based on his need to prove that the
ghost who has accused Claudius is an "honest" one—not a lying demon who might try to trick Hamlet
to lose his immortal soul by killing a king.

One of the strongest
debates about Hamlet is whether he is, in fact, insane or just pretending. Though
he tells the audience that he is only mad when "needed," his behavior is
sometimes so erratic that it is difficult to know for certain if he is as mentally sound as he
insists.

It is during the first half of the twentieth century, that
psychoanalytic theory is applied to Hamlet, by several people—in particular,
Sigmund Freud, the pioneer in explaining "the inner mental forces determining human
behavior."

Based on his study of a variety of literary theories, as well as his
own psychoanalytic theories, Freud does not concentrate on Hamlet's
"madness" as much as Hamlet's sexual href="http://dictionary.reference.com/browse/proclivities">proclivities, seen
through a psychoanalytic lens...

readability="6">

Freud concludes that Hamlet has an 'Oedipal desire for his
mother and the subsequent guilt [is] preventing him from murdering the man [Claudius] who has
done what he unconsciously wanted to
do.'

Freud also identifies Hamlet's
desire to kill Claudius as killing the "father figure" who stands in his way. Freud goes on to
explain that Hamlet's repressed sexual desires for Gertrude make him feel as sinful as Claudius,
who Hamlet describes as [a]...

readability="7">

..."incestuous, murd'rous, damned Dane."
(V.ii.335)

Freud's analysis of Hamlet
has been taken quite to heart and supported by others such as Ernest Jones and Jacques Lacan.
Freud's influence has also had an enormous influence in the way that the Prince of Denmark has
been portrayed over the years by the actors who have chosen to interpret this tragic figure as a
man with an Oedipal-complex.

H. R. Coursen insists that criticism of
Hamlet must be "psychological" in nature. However, he states that
psychoanalysis can only be subjective because it is based upon the perceptions/theories of a
particular psychoanalyst. He explains that no matter how objective the "critic" may be, he/she is
driven to answer the question presented in the first line of the play: "Who's there?" In trying
to be objective, the critic becomes subjective.

readability="5">

Any claim to critical objectivity signals an inevitable
surrender to unperceived
subjectivity.

Coursen goes on to write
that with Hamlet, all anyone can hope to do is provide a
personal response to Hamlet's character, not an objective
one.

The greatest
critics...admit their [subjectivity] and do not claim to tell us 'what
Hamlet means,' but 'what Hamlet means to
me.'

So while the most "popular"
psychoanalytic evaluation of Hamlet—by Freud—says he is a man with a secret desire for his
mother, Coursen argues that analyses of this nature reveal more about the psychoanalyst than that
of the character of Hamlet. After all, psychoanalysis as a science is a mixed bag at best,
depending on whose theory you accept.

Additional
Source:

http://www.notablebiographies.com/Fi-Gi/Freud-Sigmund.html