| 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...first by the second, plus the square of the second.** Let a represent one of the quantities, and b the other ; then a+J=their sum ; and (a+6)X (o+J), or... | |
| 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...first by the second, plus the square of the second.** • DEMONSTBATION. f Let a + b represent the sum of two quantities. Squaring it, or multiplying it... | |
| 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...FIRST BY THE SECOND, PLUS THE SQUARE OF THE SECOND.** NOTE. — This principle demands close attention. ILLUSTRATION. — What is the square of 27 ? 27 is... | |
| Charles Davies - Algebra - 1859 - 324 pages
...That is, The square of the difference of any 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. 1.** Find the square of 2a — b. We have, (2a — o)2 = 4a2 - 4ao + o2. 2. Find the square of 4аc —... | |
| Charles Davies - Algebra - 1860 - 414 pages
...b)2 = (a + 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...first by the second, plus the square of the second.** To apply this formula to finding the square of the binomial 5a2 + 8a26, we have (5a2 + 8a26)2 = 25a4... | |
| Charles Davies - Algebra - 1860 - 332 pages
...of a + b, we have, (a + by = (a + 1) (a + b) = a' + lab + b1. That is, The square of the sum of any **two quantities is equal to the square of the first,...first by the second, plus the square of the second. 1.** Find the square of 2a + 3b. We have from the rule, 63. What is a formula? What are the uses of formulas... | |
| Dana Pond Colburn - 1860 - 390 pages
...the second : The square of the sum of anil two numbers equals the square of the .first, plus tioice **the product of the first by the second, plus the square of the** tecond. Illustrations. (7 + 5)2 = 72 + 2 X 7 X 5 + 52 = 49 + 70 + 25 = 144 = 12* X 8 X 4 +42=64 + 64... | |
| Charles Davies - Algebra - 1861 - 322 pages
...6) = a2 + 2ab f b2. That ia, The square &/ the sum of two quantities is equal to the square •»f **the first, plus twice the product of the first by...plus the square of the second. 1 . Form the square of** 2a + 36. We have from the rule (2a + 36)2 = 4a2 + 12a6 + 962. 2. (aau + 3«c)2 = 25a262 + 30a26c +... | |
| 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...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 the product a'+2ab+b'. Hence, if we wish to... | |
| Thomas Sherwin - 1862 - 252 pages
...Hence the second power of the sum of two quantities contains the second power of the first quantity, **plus twice the product of the first by the second, plus the** second power of the second. Find the second power of a — 6. Operation, a — b a — b a 2 — a... | |
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