 | Rufus Putnam - Arithmetic - 1849 - 402 pages
...+ 3)*. From these examples and illustrations, wo see that the square of the sum of any two numbers is equal to the square of the first, plus twice the product of the first into the second, plus the square of the second. 5. Find by this method the square of4-f-3; 5-f-8; lf-4;... | |
 | Stephen Chase - Algebra - 1849 - 348 pages
...have (a+6) 2 = (a+J) (a+J) = a2+2ab+b2. That is, THEOREM I. The square of the sum of two numbers i> equal to the square of the first, plus twice the product of tlte Jirst by the second, plus the square of the second. Or, more briefly, The square of the sum of... | |
 | Joseph Ray - Algebra - 1852 - 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...of the first, plus twice the product of the first by the second, plus the square of the second. Let a represent one of the quantities, and b the other... | |
 | Joseph Ray - Algebra - 1848 - 250 pages
...product will be o2+2a6+62 ; thus : a+b But a-\-b is the sum of the quantities, a and b : hence THEOREM I. The square of the sum of two quantities, is equal...of the first, plus twice the product of the first by the second, plus thz square of the second. EXAMPLES. NOTE. — The instructor should read each of... | |
 | New York (State) School for the deaf, White Plains - 1854 - 936 pages
...gives minus." (b-— 1)=! (If— 1)=(&6— &s)." What is the square of the sum of two quantities T " The square of the sum of two quantities is equal to...of the first, plus twice the product of the first by the second, plus the square of the second." (la— 5Z>)S= what! " (la— 5Z>)3= 49as— 70ab+25b\"... | |
 | Jeremiah Day - Algebra - 1854 - 428 pages
...certain cases in Multiplication of frequent occurrence, and should be carefully learned. THEOREM I. The square of the Sum of two quantities is equal to...square of the first, plus twice the product of the jirst and second, plus the square of the second. This may be expressed algebraically thus, (a+b)3=a3+2ab+b3,... | |
 | James William M'Gauley - 1854 - 284 pages
...algebraic formula [sec. 1, 1], — For, the result of the multiplication may be read as follows : — " the square of the sum of two quantities is equal to the sum of their squares, plus twice their product." And as the given quantities may represent any possible... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...Required the square of 3+2 v/5. These two examples are comprehended under the rule in Art. 60, that the square of the sum of two quantities is equal to...of the first, plus twice the product of the first by the second, plus the square of the second. Ex. 3. Required the cube of ^/x+3^/y. Ex. 4. Required... | |
 | 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 +... | |
 | Elias Loomis - Algebra - 1856 - 280 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 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... | |
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The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first multiplied by the second, plus the square of the second. 
