| Dana Pond Colburn - Arithmetic - 1856 - 392 pages
...the second, and b2 equals the square of the second ; The square of the sum of any two numbers equals the square of the first, plus twice the product of the first by the second, plus the square of the tecond. Illustrations. (7 + 5)2 = 72 + 2 X 7 X 5 + S2 = 49 +... | |
| Joseph Ray - Algebra - 1857 - 408 pages
...following theorems, which may be regarded as the simplest application of Algebra. ART. 78. THEOREM I. — The square of the sum of two quantities is equal to...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 b the other... | |
| John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...+ Зааг* —х". .dn«. a'— 2ax+x\ CHAPTER III. THEOREMS AND FACTORING. 0 THEOREM I. ( 1 09.) The square of the sum of two quantities is equal to...of the first, plus twice the product of the first by the second, plus the square of the second. • DEMONSTBATION. f Let a + b represent the sum of two... | |
| Charles Davies - Algebra - 1859 - 324 pages
...a + b, we have, (a + b)' = (a + b) (a + b) = a' + <¿ab + b\ That is, The square of the sum of any two quantities is equal to the square of the first, plus twice the product of the first by (he second, plus the square of the second. 1 . Find the square of 2a + 3o. We have from the role.... | |
| Silas Lawrence Loomis - Arithmetic - 1859 - 324 pages
...language ? Repeat Prin. 1 . Illustration. Inf 356. PRIN. 2. — THE SQUARE or 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. NOTE. — This principle demands close attention. ILLUSTRATION.... | |
| James B. Dodd - Algebra - 1859 - 368 pages
...of (a+x) (a— a) 1 What is the Product of (a+5) (a— 5) 1 Of (3+y) (3— y)1 Of (x— 1) (a (59.) The Square of the sum of two quantities is equal to the sum of the squares plus twice the product of the two quantities. Thus (a+b) (a+b), that is, the square... | |
| Charles Davies - Algebra - 1860 - 412 pages
...+ b) X (a + b), or performing the multiplication indicated, (a + b)z = <£• + 2ab + 62 ; that is, The square of the sum of two quantities is equal to...of the first, plus twice the product of the first by the second, plus the square of the second. To apply this formula to finding the square of the binomial... | |
| Elias Loomis - Algebra - 1862 - 312 pages
...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 to...of 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 ab+b' we obtain... | |
| Benjamin Greenleaf - 1863 - 338 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...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... | |
| 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... | |
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