 | Benjamin Greenleaf - 1863 - 338 pages
...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 b the other; then, (a + ft)2 = (a -f- 6) X... | |
 | Charles Auguste A. Briot - 1863 - 374 pages
...SUM OF TWO NUMBERS. 156. The square of the sum of two numbers equals the square of the first number, plus twice the product of the first by the second, plus the square of the second. Be it given to raise the sum of 7 + 5 to the square ; it is necessary to multiply 7 + 5 by... | |
 | Gerardus Beekman Docharty - Algebra - 1862 - 336 pages
...THEOREM II. The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of (he second. EXAMPLES. 2. (3x-2a)'=(3x-2a)(3x-2a). Ans. 3. (9x-3y)'= Ans. 4. (6-i)'= Ans. 5. (Gt)'=... | |
 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...(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, in words,... | |
 | Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...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' Or,... | |
 | Joseph Ray - Algebra - 1866 - 250 pages
...the quantities, a and 6. Hence, 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. NOTE . — Let the pupil apply the theorem by writing the following examp\>, enunciated thus... | |
 | Benjamin Greenleaf - 1866 - 336 pages
...algebraic operations. THEOREM I. 76, The square of the sum of two quantities is equal to the tquare 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 b the other; then, (a + 6)' = (a + 6) X (a... | |
 | Joseph Ray - Algebra - 1852 - 422 pages
...THEOREM II. — The square of the difference of 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 se'vnd. Let a represent one of the quantities, and b the other ; then a — 6=their difference ; and... | |
 | Charles Davies - Algebra - 1867 - 322 pages
...6) = a2 + 2a5 f- b\ That is, The square &f the sum of two quantities is equal to the tqitart •)f the first, plus twice the product of the first by the second, plat the square of the second. 1. Form the square of 2a + 36. We have from the rule (2a + 36)2 = 4a2... | |
 | Elias Loomis - Algebra - 1868 - 386 pages
...following theorems have very important applications. The square of the sum of two numbers is equal to the square of the first, plus twice the product of the first ly the second, plus the square jof the second. Thus, if we multiply a+6 by a+6 a 2 + ab ab+b* we. obtain... | |
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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. 
