| Dana Pond Colburn - 1860 - 390 pages
...the second : The square of the sum of anil two numbers equals the square of the .first, plus tioice **the product of the first by the second, plus the square of the** tecond. Illustrations. (7 + 5)2 = 72 + 2 X 7 X 5 + 52 = 49 + 70 + 25 = 144 = 12* X 8 X 4 +42=64 + 64... | |
| Charles Davies - Algebra - 1861 - 322 pages
...b2. That ia, The square &/ the sum of two quantities is equal to the square •»f the first, plus **twice the product of the first by the second^ plus the square of the second.** 1 . Form the square of 2a + 36. We have from the rule (2a + 36)2 = 4a2 + 12a6 + 962. 2. (aau + 3«c)2... | |
| Elias Loomis - Algebra - 1862 - 312 pages
...memory. THEOREM I. The square of the sum of two quantities is equal to the square of the first, plus **twice the product of the first by the second, plus the square of the second.** Thus, if we multiply a +b by a +b a"+ ab ab+b' we obtain the product a'+2ab+b'. Hence, if we wish to... | |
| Benjamin Greenleaf - 1863 - 338 pages
...-f- 4 a4 6s. . 4. Square a3 V + 3 a2 6s c4. Ans. a" 64 + 6 a5 Jf c4 + 9 a4 6" c8. THEOREM II. 77i The **square of the difference of two quantities is equal...second. For, let a represent one of the quantities, and** 6 the other ; then, (a _ 6)2 = (a — 6) X (a — 6) = a' — 2 ab + b\ which proves the theorem. EXAMPLES.... | |
| Gerardus Beekman Docharty - Algebra - 1862 - 338 pages
...Multiply a— b by a— b. (a-by=(ab) (ab) = a'-2ab+b\ From which we deduce the following THEOREM II. The **square of the difference of two quantities is equal...product of the first by the second, plus the square of** (he second. EXAMPLES. 2. (3x-2a)'=(3x-2a)(3x-2a). Ans. 3. (9x-3y)'= Ans. 4. (6-i)'= Ans. 5. (Gt)'=... | |
| Charles Auguste A. Briot - 1863 - 376 pages
...TWO NUMBERS. 156. The square of the sum of two numbers equals the square of the first number, plus **twice the product of the first by the second, plus the square of the second.** Be it given to raise the sum of 7 + 5 to the square ; it is necessary to multiply 7 + 5 by 7 + 5. In... | |
| Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...second, plus the square of the second. II. (a— b)'=(a— ¿) (a— b)=a'— 2ab+b* Or, in words, The **square of the difference of two quantities is equal to the square of the** ßrst, minus twice the product of the first and second, plus the square of the second. III. (ti+6)... | |
| Benjamin Greenleaf - Algebra - 1864 - 336 pages
...4 a4 62. 4. Square a5 62 + 3 a2 W c4. Ans. a6 64 4- 6 a" 6" c4 4- 9 a4 66 c8. ' THEOREM II. 77. ^%e **square of the difference of two quantities is equal...of the first, minus twice the product of the first** ty the second, plus the square of the second. For, let a represent one of the quantities, and b the... | |
| Paul Allen Towne - Algebra - 1865 - 314 pages
...numerical value when a; = 8, y = 8. 63. Since (*— y) ( x -y) = (x — yf = x'-2xy+y3, it follows that The **square of the difference of two quantities is equal to the square of the first** — twice their product -\- the square of the last. EXAMPLES. 1. (« — 6)" = ^ — 2a6 + 62. 2. (2a... | |
| Joseph Ray - Algebra - 1852 - 420 pages
...proves the theorem AP PL I CAT ION. 1. (2+5)'=4+20+25=49. 2. (2m+ 3. ( 4. ( ART. 79. THEOREM II. — The **square of the difference of two quantities is equal...of the first by the second, plus the square of the** se'vnd. Let a represent one of the quantities, and b the other ; then a — 6=their difference ; and... | |
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