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.

With the fact that the Hootses can only use their " Burger King " name in the Mattoon area and that the Burger King chain can use the name in the United States excluding the Mattoon area after a 1968 trademark lawsuit, there is a 20 mile radius centering the Hootses ' Burger King, and the chain cannot have one within the radius.

* 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 peace and security established in his dominions, he convoked an assembly of the states and declared his son Malik Shah I his heir and successor.

With Portugal's position as a country firmly established, Afonso II endeavoured to weaken the power of the clergy and to apply a portion of the enormous revenues of the Roman Catholic Church to purposes of national utility.

With the dissolution of the German Confederation in 1866 and the founding of the German Empire ( Deutsches Reich ) in 1871, the Reichstag was established as the German parliament in Berlin.

With the new constitution of 1949, the Bundestag was established as the new ( West ) German parliament.

With the French army ashore, the fleet anchored in Aboukir Bay, a station northeast of Alexandria, in a formation that its commander, Vice-Admiral François-Paul Brueys D ' Aigalliers, believed established a formidable defensive position.

With a business association established with two entrepreneurs, Edward Molton and Stephen Warwick, and with John Muggeridge from Conran serving briefly as an assistant, he set about working primarily for the music industry.

With the arrival of news in May 1810 that southern Spain had been conquered by Napoleon's forces, that the Spanish Supreme Central Junta had dissolved itself, declarations of independence in Quito ( 1809 ), Gran Colombia ( 1810 ), Venezuela and Paraguay ( 1811 ) and other territories, established their own governments.

With these changes to forty-five years of established diplomacy and military confrontation, new challenges confronted U. S. policymakers.

* " With feeling profound concern, grief, indignation, am compelled disclose Bahá ' í world recent developments Holy Land furnishing further incontestable proof relationship established old and new Covenant-breakers demonstrating increasing boldness, marked, tragic decline in character and spiritual condition grandchildren ` Abdu ' l-Bahá.

With the company established and a successful product on the market, DEC turned its attention to the computer market once again as part of its planned " Phase II ".

With these funds, they established a trust to help Wheelock.

With the assistance of Seiichi Tanaka, Kinnara and Chicago taiko, the New York Buddhist church established the first taiko group on the East Coast, Soh Daiko, in 1979.

With the rise of Islam in the 7th century the power of Aksum declined and the Kingdom became isolated, the Dahlak archipelago, northern and western Eritrea, came under increasing control of Islamic powers based in Yemen and Beja lands in Sudan. The Beja were often in alliance with the Umayyads of Arabia who themselves established footholds along stretches of the Eritrean coastline and the Dahlak archipelago while the Funj of Sudan exacted tribute from the adjacent western lowlands of Eritrea.

With the 16th century Protestant Reformation the burghers became Lutherans and the first Lutheran Gymnasium was established in Elbląg in 1535.

With the passage of time, his sojourn in Japan could be considered somewhat fruitful as attested by congregations established in Hirado, Yamaguchi and Bungo.

With the creation of the creed, a precedent was established for subsequent local and regional councils of Bishops ( Synods ) to create statements of belief and canons of doctrinal orthodoxy — the intent being to define unity of beliefs for the whole of Christendom.

With some 25 million members, KdF was the largest of the many organizations established by the Nazis.

With permanent ceasefire coming into effect, Israel's new borders, later known as the Green Line, were established.

With the permission of President Thomas Jefferson, Astor established the American Fur Company on April 6, 1808.

With relations first established with the PRC in 1980, Kiribati had been the home to a satellite tracking base for China's space program from 1997 until 2003, a week before ties were formally severed.

With brilliance and diligence, he established a strong monarchy, conquered the Palestinian coast, reconciled the crusader barons, and built strong frontiers against the kingdom's Muslim neighbours.

With this established, he invented a process in which liquids such as milk were heated to kill most bacteria and moulds already present within them.

With sacrifice and priesthood established, chapters 11 – 15 instruct the lay people on purity ( or cleanliness ).

With Macau's low-cost operating environment and its surplus quotas under the Multi Fiber Arrangement ( MFA ), many Hong Kong industrialists established textile and garment manufacturing bases in Macau.

With the exploration of the West, mining camps were established and " expressed a distinctive spirit, an enduring legacy to the new nation ;" Gold Rushers would experience the same problems as the Land Rushers of the transient West that preceded them.