 | 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.... | |
 | Joseph Ray - Algebra - 1866 - 252 pages
...square of the difference of two quantities is equal to the square of the first, minus twice the prodnet of the first by the second, plus the square of the second. 1. (5— 4)2=25— 40+16=1. 2'. (2a— 6)2=4a2— 3. (3a!— 2yy=9x*-— 4. (x*— y*y=tf 5. (ax—... | |
 | 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... | |
 | Elias Loomis - Algebra - 1868 - 312 pages
...following theorems are of such extensive application that they should be carefully committed to memory. THEOREM I. The square of the sum of two quantities is equal io the square of the first, plus twice the product of (he first by the second, plus the square of the... | |
 | Robert Wallace - 1870 - 164 pages
...example the following theorem for finding the square of the sum of a,ny two quantities is deduced. THEOREM I. — The square of the sum of two quantities...first by the second, plus the square of the second. EXAMPLES. 1. 2. 3. 4. 5. 0. 2oa;+4a2. Ans. Ans. Ans. Ans. „. 6+J)2=36--3+,4i7=39TIcT. Ane. 24. Multiply... | |
 | Benjamin Greenleaf - 1870 - 334 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 square of the firsl, plus twice the product of the first by the second, plus the square of the second. For, let a... | |
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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. 
