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 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 the advent of recorded music and radio, " Amazing Grace " began to cross over from primarily a gospel standard to secular audiences.

With the advent of wireless and radio goods, people came to be much more connected.

With improved radio telescopes, hydrogen gas could also be traced in other galaxies.

With help from supporters Senator Dill and Representative White, Hoover brought the issue of radio control to the Senate floor.

With 24 optical and two radio telescopes, it is the largest, most diverse gathering of astronomical instruments in the world.

With the addition of an additional radio frequency pulse and additional manipulation of the magnetic gradients, a T < sub > 2 </ sub >- weighted sequence can be converted to a FLAIR sequence, in which free water is now dark, but edematous tissues remain bright.

With these satellites in place China's domestic satellite communication network went into operation, facilitating television and radio transmissions and providing direct-dial longdistance telephone, telegraph, and facsimile service.

With a radio advertising campaign featuring the jingle " Pepsi-Cola hits the spot / Twelve full ounces, that's a lot / Twice as much for a nickel, too / Pepsi-Cola is the drink for you ", arranged in such a way that the jingle never ends.

With the rise of radio, Pepsi utilized the services of a young, up-and-coming actress named Polly Bergen to promote products, oftentimes lending her singing talents to the classic "... Hits The Spot " jingle.

In Australia, where Robyn reached the top ten of the iTunes Store's album chart, " With Every Heartbeat " received substantial attention on radio and video networks in Australia.

" With Every Heartbeat ", " Handle Me " and " Cobrastyle " were top ten club hits, and the former received airplay at US pop and dance radio stations.

Bob Dylan marked Orbison as a specific influence, remarking that there was nothing like him on radio in the early 1960s: With Roy, you didn't know if you were listening to mariachi or opera.

With conservative talk radio host Marshall Gilbert as his campaign manager, Bono placed a successful bid to become the new mayor of Palm Springs.

With funding from the Norwegian government, radio continued to broadcast live throughout.

With few exceptions, radio stations east of the Mississippi River received official call signs beginning with the letter W ; those west of the Mississippi a K. The amount of programs these early stations aired was often limited, in part due to the expense of program creation.

With a radio operator initiating a call, the process normally takes a few minutes for the ALE to pick an HF frequency that is optimum for both sides of the communication link.

With a weekly radio broadcast, famous white clientele nightly poured in to see them.

With the outbreak of the First World War in 1914, he offered his services to the army in the development of radio communications.

With over 16, 800 episodes, it is both the world's longest running radio soap and, since the cancellation of the American soap opera Guiding Light in September 2009, the world's longest running soap opera in any format.

With sparked interest in the song, radio stations began playing the studio version of " Pardon Me ".

With no visual component, radio drama depends on dialogue, music and sound effects to help the listener imagine the characters and story.

With the advent of television in the 1950s, however, radio drama lost some of its popularity, and in some countries, has never regained large audiences.

With 21st-century technology, modern radio drama, also known as audio theater, has experienced a revival, with a growing number of independent producers who are able to build an audience through internet distribution.

With its three services, News & Information, Classical Music and The Current, MPR operates a 43-station regional radio network in the upper Midwest serving over 9 million people.