 | Benjamin Greenleaf - 1866 - 336 pages
...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. For, let a represent one of the quantities, and b the other; then, (a + 6)' = (a + 6) X (a + V) = a3... | |
 | Education - 1866 - 538 pages
...and research, we come fully to comprehend the truth that •' 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" ; and when the tyro in Algebra jabbers off this formula, we vainly... | |
 | Joseph Ray - Algebra - 1852 - 422 pages
...THEOREM II. — The square of the difference of two quantities is equal to the square of the first, minus twice the product 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... | |
 | 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—... | |
 | William Rossiter - 1867 - 250 pages
...64. Or, substituting general symbols for particular numbers : Or, expressing the theorem in words, the square of the sum of two numbers is equal to the sum of the squares of the same numbers, together with twice their product. Bearing this in mind, we... | |
 | 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... | |
 | Elias Loomis - Algebra - 1868 - 386 pages
...19(6— c)— 6. Expand and reduce 66. The three following theorems have very important applications. The square of the sum of two numbers is equal to the...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... | |
 | 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... | |
 | Webster Wells - Algebra - 1908 - 262 pages
...required to square a +b. a+b a+b a3+ ab ab + b2 That is, the square of the sum of two numbers equals the square of the first, plus twice the product of...first by the second, plus the square of the second. 1 . Square 3 a + 2 b. We have, (3 o + 2 6)2 = (3 a)2 + 2(3 a) (2 6) + (2 6)2 Let it be required to... | |
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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. 
