 | Benjamin Greenleaf - Algebra - 1879 - 322 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...first by the second, plus the square of the second. For, let a represent one of the quantities, and b the other; then, (a + b)' = (a + 4) X (a + 6) = a2... | |
 | Benjamin Greenleaf - Algebra - 1879 - 352 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. Define a Formula. What is Theorem I. ? For, let a represent one of the quantities, and b the other;... | |
 | Elias Loomis - Algebra - 1879 - 398 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 by the second, plus Hie square of the second. Thus, if we multiply a+b by a + b a? + ab ab + b2 we obtain the product a2... | |
 | Webster Wells - Algebra - 1879 - 468 pages
...is, (a + bY = a? + 2ab + b2. (1) The square of the sum of two quantities is equal to the square nf the first, plus twice the product of the first by the second, plus the square of the second. 105. "We may also show, by multiplication, that (a — 6)2 = a2 — 2 ab + b2. (2) That is, The square... | |
 | Shelton Palmer Sanford - Algebra - 1879 - 348 pages
...THEOKEM H. 68. 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 second. Ex. 1. Find the square of (a — 6). Analysis. Here a and 6 are the two quantities, and OPERATION (a... | |
 | Benjamin Greenleaf - Algebra - 1879 - 376 pages
...THEOREM II. 77. 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 tfte second. For, let a represent one of the quantities, and 6 the other; then, (a — 6)a = (a —... | |
 | Joseph Ray - Arithmetic - 1880 - 420 pages
...operations illustrate the following principle : PRINCIPLE. — The square of the sum of two numbers is equal to the square of the first, plus twice the...first by the second, plus the square of the second. Thus : Show by involution, that : \. (5)2 equals 25. 8. (£)5 equals MrlJ. 2. 14s 2744. 9. (.02) s... | |
 | Webster Wells - Algebra - 1880 - 512 pages
...That is, 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 second. 106. Again, by multiplication, we have (a + b) (a - b) = a2 - V. (3) That is, The product of the sum... | |
 | Charles Scott Venable - Algebra - 1880 - 168 pages
...expresses the Rule :—Tlie square of the difference of two quantities is the square of the first, minus twice the product of the first by the second, plus the square of the second. Ex. 1. (x - 5)" = x' - 10ж + 25. Ex. 2. (За - 2o)" = (За)' - 2 x За х 2o + (2o)' = 9a' - 12ao... | |
 | Joseph Ray - Arithmetic - 1880 - 420 pages
...following principle : PRINCIPLE. — The square of the sum of two numbers is equal to the square of Hie first, plus twice the product of the first by the second, plus tiie square of the second. Thus : Show by involution, that: 1. (5)2 equals 25. 8. a)5 equals ttm2.... | |
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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. 
