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" The square of the sum of two quantities is equal to the square nf the first, plus twice the product of the first by the second, plus the square of the second. "
The first principles of algebra, for the use of the boys of the Royal ... - Page 23
by Admiralty - 1845
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Elements of Algebra

Charles Davies - Algebra - 1842 - 368 pages
...the binomial, (a-\-b). We have, from known principles, (a + b)2=(a+b) (a+i)=a 2 +2ai+i 2 . 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....
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An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - Algebra - 1845 - 308 pages
...14a26c5+14a62c5— 3a2ce— 7 16. Multiply a+6 by a+b. The product is a2+2a6-}-62; from which it appears, that 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....
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Elements of Algebra: Including Sturms' Theorem

Charles Davies - Algebra - 1845 - 382 pages
...the multiplication of algebraic quantities in the demonstration of the following theorems. 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....
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 380 pages
...2. Required the square of 3 + 2 A/ 5. These two examples are comprehended under the rule in Art. 60, that 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....
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 376 pages
...2. Required the square of 3 + 2 \/ 5. These two examples are comprehended under the rule in Art. 60, that 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....
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 250 pages
...be a2+2a6+62; thus: a+6 a+6 a2+a6 But a-\-b IB the sum of 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....
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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1848 - 302 pages
...to form the square or second power of the binomial (a-\-b). We have, from known principles, 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....
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Elements of Algebra

James Haddon - Algebra - 1850 - 210 pages
...3a,6+3a6,+&' =a>+b,+8ab(a+b) =a'-が-3aあ(a-あ). Hence, by the last two formul,e, the cube of the sum of two quantities is equal to the sum of their cubes + three times their product multiplied by their sum. ⅠⅠ ノ 石 Ⅹ ノ 圧 言 二 叫 皿...
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Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

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 the square of the first, plus twice the product of the first by the second, plus the square of the second....
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

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 to the square of the first, plus twice the product of the first by the second, plus thz square of the second....
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