 | Joseph Ray - Algebra - 1857 - 408 pages
...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 the square 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... | |
 | John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...—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 the square of the first, plus twice the product of the first by the second, plus the square of the second. • DEMONSTBATION. f Let a + b represent the sum... | |
 | Jeremiah Day - Algebra - 1859 - 422 pages
...Multiplication of frequent occurrence, and should be carefully learned. THEOREM I. 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. This may be expressed algebraically thus, (a+b)3 =a3... | |
 | Charles Davies - Algebra - 1859 - 324 pages
...a + b, we have, (a + b)' = (a + b) (a + b) = a' + <¿ab + b\ That is, The square of the sum of any two quantities is equal to the square of the first, plus twice the product of the first by (he second, plus the square of the second. 1 . Find the square of 2a + 3o. We have from the... | |
 | 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 PRODUCT OF THE FIRST BY THE SECOND, PLUS THE SQUARE OF THE SECOND. NOTE. — This principle demands close attention.... | |
 | Charles Davies - Algebra - 1860 - 412 pages
...performing the multiplication 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 the first by the second, plus the square of the second. To apply this formula to finding the square of... | |
 | Elias Loomis - Algebra - 1862 - 312 pages
...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 of the first by the second, plus the square of the second. Thus, if we multiply a +b by a +b a"+ ab ab+b'... | |
 | Benjamin Greenleaf - 1863 - 338 pages
...give rise to formulas, useful in abridging algebraic operations. THEOREM I. 76 ( 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. For, let a represent one of the quantities, and... | |
 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...which follow: I. (a+b)'=(a+u) (a+b')=a>+2ab+bt Or, expressing the result in words, 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. II. (a— b)'=(a— ¿) (a— b)=a'— 2ab+b* Or,... | |
 | Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...operations, the results which foltow: Or, expressing the result in words, The square of the sum of tico quantities is equal to the square of the first, plus twice the product of the first -and second, plus the square of the second. . • II. (a— b)'=(a— u) (a— b) = at— 2ab+b'... | |
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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. 
