 | Joseph Ray - 1848 - 250 σελίδες
...divisible by a — b, then will am—bm be also divisible by it. That is, IF the difference oflfu same powers of two quantities is divisible by the difference of the quantities themselves, then will tlie difference of the next higher powers of the same quantities, be divisible... | |
 | Joseph Ray - 1852 - 408 σελίδες
...divisible by a — b, then will a™ — im,be divisible by a — b. That is, IF the difference of the same powers of two quantities is divisible by the difference of the quantities themselves, then will the difference of the next higher powers of the same quantities, be divisible... | |
 | Joseph Ray - 1852 - 422 σελίδες
...divisible by a — b, then will a1"— 6m,be divisible by a — 4. That is, IF the difference of the same powers of two quantities is divisible by the difference of the quantities themselves, then win the difference of the next higher powers of the same quantities, be divisible... | |
 | William Frothingham Bradbury - 1868 - 264 σελίδες
...— y5) H- (a; — y) = x4 + a;'y + x2/ + xf + y4 By I. of this article, the difference of the same powers of two quantities is divisible by the difference of the quantities; therefore x — y must be a factor of x5 — if ; and dividing a^ — y6 by x — y gives the other... | |
 | Elias Loomis - 1868 - 386 σελίδες
...a—5, it is obvious that the dividend is divisible by a—b; that is, if the difference of the same powers of two quantities is divisible by the difference of the quantities, then will the difference of the powers of the next higher degree be divisible by that difference. divisible... | |
 | Joseph Ray - 1866 - 420 σελίδες
...6, then will the quantity am— bm be divisible by a — b. That is, If the difference of (he same powers of two quantities is divisible by the difference of the quantities themselves, then will the difference of the next higher powers of the same quantities be divisible... | |
 | Daniel Barnard Hagar - 1873 - 278 σελίδες
...second. 2. Eesolve 9a2 — 6ac + c2 into two equal factors. 3. Show that the difference of any two equal powers of two quantities is divisible by the difference of the quantities. 4. Resolve a"+x3 into two factors. 5. What is the least common multiple of y3 — 1 and y2 + x —... | |
 | Elias Loomis - 1873 - 396 σελίδες
...a— b, it is obvious that the dividend is divisible by a— b; that is, if the difference of the same powers of two quantities is divisible by the difference of the quantities, then will the difference of the powers of the next higher degree be divisible by that difference. divisible... | |
 | Joseph Ficklin - 1874 - 446 σελίδες
...r- = a8 — a?b + ab* — b3; whence, a4— o4 = a + о (a + b) (a3 - a*b + ab" —b3). 97. The sum of any two like odd powers of two quantities is divisible by the sum of the quantities (87). Thus, = a2— ab + t?; whence, a3 + b*= (a + b) (a3— ab + V). а ~т~... | |
 | Charles Mansford - 1875 - 110 σελίδες
...odd powers of two quantities is divisible by the sum of the quantities, and II. The difference of the odd powers of two quantities is divisible by the difference of the quantities ; also III. The difference of the even powers of two quantities is divisible both by the sum and difference... | |
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The difference of two like even powers of two quantities is divisible by the sum of the quantities, and... 
