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" 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 second. "
New Elementary Algebra: Designed for the Use of High Schools and Academies - Page 54
by Benjamin Greenleaf - 1879 - 309 pages
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Arithmetic and Its Applications: Designed as a Text Book for Common Schools ...

Dana Pond Colburn - 1860 - 390 pages
...the second : The square of the sum of anil two numbers equals the square of the .first, plus tioice 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 = 12* X 8 X 4 +42=64 + 64...
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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1861 - 322 pages
...b2. That ia, The square &/ the sum of two quantities is equal to the square •f the first, plus twice the product of the first by the second^ plus the square of the second. 1 . Form the square of 2a + 36. We have from the rule (2a + 36)2 = 4a2 + 12a6 + 962. 2. (aau + 3c)2...
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The Elements of Algebra: Designed for Beginners

Elias Loomis - Algebra - 1862 - 312 pages
...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' we obtain the product a'+2ab+b'. Hence, if we wish to...
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New Elementary Algebra: in which the First Principles of Analysis are ...

Benjamin Greenleaf - 1863 - 338 pages
...-f- 4 a4 6s. . 4. Square a3 V + 3 a2 6s c4. Ans. a" 64 + 6 a5 Jf c4 + 9 a4 6" c8. THEOREM II. 77i The square of the difference of two quantities is equal...second. For, let a represent one of the quantities, and 6 the other ; then, (a _ 6)2 = (a — 6) X (a — 6) = a' — 2 ab + b\ which proves the theorem. EXAMPLES....
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The Institutes of Algebra: Being the First Part of a Course of Mathematics

Gerardus Beekman Docharty - Algebra - 1862 - 338 pages
...Multiply a— b by a— b. (a-by=(ab) (ab) = a'-2ab+b\ From which we deduce the following THEOREM II. The square of the difference of two quantities is equal...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)'=...
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Elements of arithmetic, tr. by J. Spear

Charles Auguste A. Briot - 1863 - 376 pages
...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 7 + 5. In...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...second, plus the square of the second. II. (a— b)'=(a— ) (a— b)=a'— 2ab+b* Or, in words, The square of the difference of two quantities is equal to the square of the rst, minus twice the product of the first and second, plus the square of the second. III. (ti+6)...
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New Elementary Algebra: In which the First Principles of Analysis are ...

Benjamin Greenleaf - Algebra - 1864 - 336 pages
...4 a4 62. 4. Square a5 62 + 3 a2 W c4. Ans. a6 64 4- 6 a" 6" c4 4- 9 a4 66 c8. ' THEOREM II. 77. ^%e square of the difference of two quantities is equal...of the first, minus twice the product of the first ty the second, plus the square of the second. For, let a represent one of the quantities, and b the...
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Algebra: Adapted to the Course of Instruction Usually Pursued in the ...

Paul Allen Towne - Algebra - 1865 - 314 pages
...numerical value when a; = 8, y = 8. 63. Since (*— y) ( x -y) = (x — yf = x'-2xy+y3, it follows that The square of the difference of two quantities is equal to the square of the first — twice their product -\- the square of the last. EXAMPLES. 1. ( — 6)" = ^ — 2a6 + 62. 2. (2a...
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Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

Joseph Ray - Algebra - 1852 - 420 pages
...proves the theorem AP PL I CAT ION. 1. (2+5)'=4+20+25=49. 2. (2m+ 3. ( 4. ( ART. 79. THEOREM II. — The square of the difference of two quantities is equal...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...
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