 | Elias Loomis - Algebra - 1855 - 356 pages
...are comprehended under the rule in Art. 60, that the square of the sum of two quantities is equal to the square of the first, plus twice the product of...first by the second, plus the square of the second. Ex. 3. Required the cube of ^/x+3^/y. Ex. 4. Required the fourth power of v/3— ^2. Ans. 49— 20V"?.... | |
 | Dana Pond Colburn - Arithmetic - 1855 - 396 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 + 52 = 49 + 70 + 25 = 144 = 122 (8 -f- 4)a = 82 +... | |
 | 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 + 70 + 25 = 144 = 12» (8 + 4)2 = 82 + 2... | |
 | Elias Loomis - Algebra - 1856 - 280 pages
...square of the sum of two quantities is equal to the square of the first, plus twice the product oj 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 the product a'+2ab+b'. Hence, if we wish to obtain... | |
 | Joseph Ray - Algebra - 1857 - 408 pages
...application of Algebra. ART. 78. THEOREM I. — The square of the sum of two quantities is equal to the square of the first, plus twice the product of...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... | |
 | Silas Lawrence Loomis - Arithmetic - 1859 - 324 pages
...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...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... | |
 | John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...III. THEOREMS AND FACTORING. 0 THEOREM I. ( 1 09.) The square of the sum of two quantities is equal to the square of the first, plus twice the product of...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... | |
 | 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 - 330 pages
...= (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, plus twice the product of...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... | |
 | Charles Davies - Algebra - 1860 - 412 pages
...indicated, (a + b)z = <£• + 2ab + 62 ; that is, The square of the sum of two quantities is equal to the square of the first, plus twice the product of...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... | |
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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. 
