For positive values of a and b, the binomial theorem with n = 2 is the geometrically evident fact that a square of side can be cut into a square of side a, a square of side b, and two rectangles with sides a and b. With n = 3, the theorem states that a cube of side can be cut into a cube of side a, a cube of side b, three a × a × b rectangular boxes, and three a × b × b rectangular boxes.

With the subsequent development of protease inhibitors and highly active antiretroviral therapy, numerous studies have documented the fact that anti-HIV drugs prevent the development of AIDS and substantially prolong survival, further disproving the claim that these drugs " cause " AIDS.

With inflation hitting 33 percent in 1990, there was, in fact, a negative real interest rate, but this situation reversed in 1991 when rates were high relative to inflation.

With the exception of the possible CCA cryptographic attack described in the limitations section below, the attacker can only know the fact that a connection is taking place between the two parties, already known to him, the domain name and IP addresses.

With such purpose, this novel concerns a dejected researcher ( Roquentin ) in a town similar to Le Havre who becomes starkly conscious of the fact that inanimate objects and situations remain absolutely indifferent to his existence.

With the fact that radio signals, newspapers and magazines from Hong Kong are available in Macau, the local media are always a minority group in terms of sales and number of viewers.

With the omission of the law of the excluded middle as an axiom, the remaining logical system has an existence property which classical logic does not: whenever is proven constructively, then in fact is proven constructively for ( at least ) one particular, often called a witness.

With the arrival of the year 2012, Nostradamus's prophecies started to be co-opted ( especially by the History Channel ) as evidence suggesting that the end of the world is imminent, notwithstanding the fact that his book never mentions the end of the world, let alone the year 2012.

With time witnesses began to appear in court they were not so treated despite the fact that their functions were akin to that of modern witnesses.

With Clemente fast becoming a fan favorite, there would seem little not to like about the early progress of his highly touted rookie season, but the transition from Puerto Rico to Pittsburgh was, in fact, anything but smooth.

With this theory, linguists can better deal with the fact that subtle differences in word meaning correlate with other differences in the syntactic structure that the word appears in.

With an approximate age of 46, 000 years, the remains consist of a pair of fragmented human jaws, but it is disputed whether these early humans were in fact Homo Sapiens or Neanderthals.

With the 602 cc engine, the tax classification of the car changed so that it became in fact a 3CV, but the commercial name remained unchanged.

* In chapter five, after bemoaning the fact that people do not appreciate landscape paintings anymore, Mr. Eager misquotes William Wordsworth's poem title ," The World Is Too Much With Us ", saying " The world is too much for us.

With regard to the fact that he wrote in English, Humphreys refers to " using the language of cultural supremacy to try to express something that comes directly from the suppressed native culture " of Wales.

In fact, Sloan's memoir and management treatise, My Years With General Motors, foresaw some of these problems.

With the late October deadline approaching in 2006, it was regarded as very unlikely that the election would in fact be held by that point, and the opposition and the rebels rejected the possibility of another term extension for Gbagbo.

On Octave Hayward had some four solo composed songs ( more in fact than on " The Other Side of Life " later in 1986 ), Edge contributed " I'll Be Level With You " ( aka " Little Man ") one of only a number of songs showing a complete group unity.

With Crowley's editions, the poem followed an existing and subsequently repeated convention of titling the poem The Vision of Piers Pierce Plowman, which is in fact the conventional name of just one section of the poem.

With the world in turmoil I now feel that a boy your age should experience what is coming his way — fully digest it without getting a " belly ache ," so to speak, nor getting off the right track of truth, fact, honesty, fair play, and being above board — never a sneak.

With Sisko's advice, Jadzia manages to bring Curzon down a peg and he finally confesses he has in fact been in love with her.

With the exception of calcium, boiling does not remove solutes of higher boiling point than water and in fact increases their concentration ( due to some water being lost as vapour ).

With only 14 participants the study lacks the statistical power to detect health improvements, and perhaps the simple fact that these 14 individuals knew that they were on a diet program made them more aware of weight and exercise regime, skewing the results

With CA problems arise in the fact that if farms do not produce as much as conventional ways, then in this case leaves the world with less food for more people.

With this no loyal citizen can quarrel.

With these keen `` eyes '' and small nuclear weapons delivered with accuracy, military forces can be directly attacked with minimum damage to urban areas.

With them, you can carry steaks and hamburgers at refrigerator temperatures, and also get your frozen food for stews and chowders, to the marina or picnic, in A-1 condition.

With such a program you can make constructive selections of the best sites available.

`` With a 15,500-lb. fork-lift, dealers can unload unitized lumber from wide-door box cars for $.30/mbf compared with $1.65 or more to unload loose lumber one piece at a time '', says James Wright of Aj.

With the above results we can make the following remarks about the graph of F.

With respect to those countries whose leaders prefer to live with their illusions, we can afford to wait, for in time their comparative lack of progress will become clear for all to see.

With a few important and a few more unimportant exceptions, no expression can be deemed le mot juste for its context, because each was very probably the only expression that long-established practice and ease of rapid recitation would allow.

With integration, the effect of a small acceleration ( or small platform tilt angle ) can be seen after a time.

With the gyro-stabilized platform leveled, it can be headed in the proper direction by using surveying techniques.

With its power to investigate, the Senate can paralyze the Secretary by keeping him in a state of perpetual testimony before committees, as it did with Dean Acheson.

With an art that almost conceals art, J. D. Salinger can create a fictional world so authentic that it hurts.

With harvests in full swing, you can enjoy festivals for grapes at Sonoma, Calif. ( Sept. 22-24 ), as well as for cranberries at Bandon, Ore. ( Sept. 28 thru Oct. 1 ), for buckwheat at Kingwood, W. Va. ( Sept. 28-30 ), sugar cane at New Iberia, La. ( Sept. 29 thru Oct. 1 ) and tobacco at Richmond, Va. ( Sept. 23-30 ).

With a few exceptions, adult amphibians are predators, feeding on virtually anything that moves that they can swallow.

With more advanced equipment, but still cheap in comparison to professional setups, amateur astronomers can measure the light spectrum emitted from astronomical objects, which can yield high-quality scientific data if the measurements are performed with due care.

A choice function is a function f, defined on a collection X of nonempty sets, such that for every set s in X, f ( s ) is an element of s. With this concept, the axiom can be stated:

With this alternate notion of choice function, the axiom of choice can be compactly stated as

With two or more equally determined players, this can result in a " bidding war " where the attribute is driven up by increments to large sums.

With some simplifications, in particular constant density, they can be given as follows:

With the foremost anchor reducing the load on the aft-most, this technique can develop great holding power and may be appropriate in " ultimate storm " circumstances.

With Edward Frankland he found that nitriles can be hydrolyzed to the corresponding acids.

With improv, people can find true expressive freedom since they don't ever know how the situation is going to turn out.

With the axiom of dependent choice ( which is a weakened form of the axiom of choice ), this result can be reversed: if there are no such infinite sequences, then the axiom of regularity is true.

With modern instrumentation these tests are rarely used but can be useful for educational purposes and in field work or other situations where access to state-of-the-art instruments are not available or expedient.