| 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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