 | 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 - 412 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 - 330 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 - Arithmetic - 1860 - 388 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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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. 
