 | Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...operations, the results which foltow: Or, expressing the result in words, The square of the sum of tico quantities is equal to the square of the first, plus twice the product of the first -and second, plus the square of the second. . • II. (a— b)'=(a— u) (a— b) = at— 2ab+b' Or,... | |
 | Benjamin Greenleaf - Algebra - 1864 - 420 pages
...and b represent any two quantities whatever, then, (a + 1)* = (a + I) (a + 4) = a2 -f 2ai + #. (1) That is, The square of the sum of two quantities is equal to t/ie sguare of the first, plus, twice the product of the first l»j the second, plus the square of... | |
 | Paul Allen Towne - Algebra - 1865 - 314 pages
...4, and a; + 7 by a; — 4. 62. Since (x + y) (x + y) = (x + y)3 = x3 + 2xy + y3,it follows th at J%e square of the sum of two quantities is equal to the square of the jirst + twice their product + the square of the last. EXAMPLES. 1. (a + 6)3 = a2 + 2a6 + 43. 2. (2a... | |
 | Education - 1866 - 538 pages
...on their way." After careful thought and research, we come fully to comprehend the truth that •' the square of the sum of two quantities is equal to...square of the first, plus twice the product of the two, plus the square of the second" ; and when the tyro in Algebra jabbers off this formula, we vainly... | |
 | John Fair Stoddard, William Downs Henkle - Algebra - 1866 - 546 pages
...10aV+5o«4— if by a1— Sa'x + Sox1 «. a1— CHAPTER III. THEOKEMS AND FACTORING. THEOREM I. . (1O9.) The square of the sum of two quantities is equal to the square of the fast, plus twice the product of tke first ky tlte second, plus the square of the second. DEMONSTRATION.... | |
 | Benjamin Greenleaf - 1866 - 336 pages
...following theorems give rise to formulas, useful in abridging algebraic operations. THEOREM I. 76, The square of the sum of two quantities is equal to the tquare of the first, plus twice the product of the first by the second, plus the square of the second.... | |
 | Charles Davies - Algebra - 1867 - 322 pages
...6) = a2 + 2a5 f- b\ That is, The square &f the sum of two quantities is equal to the tqitart •)f the first, plus twice the product of the first by the second, plat the square of the second. 1. Form the square of 2a + 36. We have from the rule (2a + 36)2 = 4a2... | |
 | William Frothingham Bradbury - Algebra - 1868 - 270 pages
...x" -j- 3 y and difference 5 x2 — 3y. 6. Sum 2 a — 8b and difference 10 a + 1* b. THEOREM II. 58. The square of the sum of two quantities is equal to...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... | |
 | William Frothingham Bradbury - Algebra - 1868 - 264 pages
...difference 5 x2 — 3 y. 6. Sum 2 a — 8 b and difference 10 a + 14 5. THEOREM II. 58. The square of (he 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... | |
 | Elias Loomis - Algebra - 1868 - 386 pages
...The three following theorems have very important applications. The square of the sum of two numbers is equal to the square of the first, plus twice the product of the first ly the second, plus the square jof the second. Thus, if we multiply a+6 by a+6 a 2 + ab ab+b* we. obtain... | |
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The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first and second, plus the square of the second. 
