 | 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,... | |
 | 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... | |
 | Joseph Ray - Algebra - 1866 - 250 pages
...will be a2+2a6-j-62. Thus: a+6 a+6 a2+2a6-|-62 But a+6 is the sum of the quantities, a and 6. Hence, Theorem I. — The square of the sum of two quantities...first by the second, plus the square of the second. NOTE . — Let the pupil apply the theorem by writing the following examp\>, enunciated thus : What... | |
 | Jeremiah Day - 1866 - 434 pages
...to certain cases in ultiplication of frequent occurrence, and should be care- ' fully" le'arned. .. THEOREM I. ' The square of the Sum of two quantities...of the first, plus twice the product of the first and second, plus the square of the second. This may be expressed algebraically thus, (a+b)3=a3+2ab+b3,... | |
 | 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.... | |
 | Joseph Ray - Algebra - 1866 - 420 pages
...certain general truths. The following theorems serve to show some of its most simple applications. 78. Theorem I. — The square of the sum of two quantities is equal to tlte square of the Jirst, plus twice the product of the Jirst by the second, plus the square of the... | |
 | Joseph Ray - Algebra - 1852 - 422 pages
...prove the following theorems, which may be regarded as the simplest application of Algebra. ART. 7§. THEOREM I. — The square of the sum of two quantities is equal to Ihe square of the Jirst, plus twice the product of the first by Hie second, plus Ihe square of the... | |
 | 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... | |
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That is, 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. 
