 | William Frothingham Bradbury - Algebra - 1868 - 270 pages
...Sum 2 a — 8b and difference 10 a + 1* b. THEOREM II. 58. The square of the sum of two quantities is equal to the square of the first, plus twice the product of the two, plus the square of the second. Let a and 6 represent the two quantities ; their sum will be a... | |
 | Richard Wormell - Geometry, Modern - 1868 - 286 pages
...difference of the squares of two numbers is equal to the product of their sum and difference. and. The square of the sum of two numbers is equal to the sum of the squares together with twice the product. 3rd. The square of the difference of two numbers... | |
 | Robert Wallace - 1870 - 164 pages
...of the sum of a,ny two quantities is deduced. 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. EXAMPLES. 1. 2. 3. 4. 5. 0. 2oa;+4a2. Ans. Ans. Ans. Ans. „.... | |
 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...difference of the squares of two numbers is equal to the product of their sum and difference. znd. The square of the sum of two numbers is equal to the sum of the squares together with twice the product. 3rd. The square of the difference of two numbers... | |
 | Joseph Ray - Algebra - 1866 - 420 pages
...show some of its most simple applications. 78. 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. Let a represent one of the quantities, and ba +6 the other.... | |
 | Benjamin Greenleaf - Arithmetic - 1871 - 350 pages
...the parts separately hy the width ? Fig. 2. 25 feet. V 20 Ew* r 6 \JC b sir D F 20 20 20 5 400 100 the square of the sum of two numbers is equal to the squares of the numbers, pins twice their product. Thus, 25 being equal to 20-1-5, its square is equal... | |
 | Horatio Nelson Robinson - Algebra - 1872 - 436 pages
...resulte which follow: Or, expressing the result in words, The »guare of the sum of two quantities is equal to the square of the first, plus twice the product of the ßrst and second, plus the square of the second. II. (a— 6)'=(o— b) (a— 6)=a'— 2ab+b' Or, in... | |
 | Elias Loomis - Algebra - 1873 - 396 pages
...reduce 53(a-6+c)-27(a+6-c)-26(a-6-c). 66. The three following theorems have very important applications. The square of the sum of two numbers is equal to 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 we obtain the product... | |
 | David White Goodrich - Ready-reckoners - 1873 - 220 pages
...the squares of 20, 30, 40, 50, etc., are 400, 900, 1600, 2500, etc. Now since -(a+b)*=a'+2ab.+ b', the square of the sum of two numbers is equal to the...first, plus twice the product of the first by the second, plus the square of the second. Thus 212 = 20'+ 2(20+ 1) + 1 = 400+40+ 1 = 441. So 105* —... | |
 | Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...methods derived from the following theorems : Tfieorem I. 113. 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, For, let a and 6 represent two quantities, then a + b will denote... | |
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The square of the sum of two numbers is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second. 
