 | 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 - 1848 - 250 pages
...itself, the 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,...twice the product of the first by the second, plus thz square of the second. EXAMPLES. NOTE. — The instructor should read each of the following examples... | |
 | Jeremiah Day - Algebra - 1854 - 428 pages
...relate to certain cases in Multiplication of frequent occurrence, and should be carefully learned. THEOREM I. The square of the Sum of two quantities...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... | |
 | 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 +... | |
 | Thomas Sherwin - Algebra - 1855 - 262 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 — 6 a — 6 • a2 —... | |
 | Elias Loomis - Algebra - 1856 - 280 pages
...following theorems are of such extensive application that they should be carefully committed to memory. THEOREM I. The square of the sum of two quantities...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... | |
 | 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... | |
 | Charles Davies - Algebra - 1857 - 408 pages
...(a + b) X (a + b), or performing the multiplication indicated, (a + b)2 = a2 + 2a6 + b2 ; that is, The square of the sum of two quantities is equal to...plus twice the product of the first by the second, plui the square of the second. To apply this formula to finding ' the square of the binomial 5a2 +... | |
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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 and second, plus the square of the second. 
