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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. "
Ray's Algebra, Part First: On the Analytic and Inductive Methods of ... - Page 64
by Joseph Ray - 1848 - 240 pages
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Elements of Algebra

William Smyth - Algebra - 1830 - 278 pages
...power or square of the sum of two quantities contains the square of the first quantity, plus double the product of the first by the second, plus the square of the second. Thus, (7 + 3) (7 + 3) or, (7 + 3)' = 49 + 42 + 9 = 100 So also (5 a2 + 8 a2 6)2 = 25 a6 + 80 <tb +...
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Elements of Algebra: Tr. from the French of M. Bourdon, for the ..., Volume 1

Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 446 pages
...enunciated in another manner : viz. The square of any polynomial contains the square of the first term, plus twice the product of the first by the second, plus the square of the second; plus twice the product of each of the two first terms by the third, plus the square of the third; plus...
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Elements of Algebra: Tr. from the French of M. Bourdon. Revised and Adapted ...

Charles Davies - Algebra - 1835 - 378 pages
...principles, (a+by=(a+b) (a+b)=a3+'2ab+b3. That is, the square of the sum of two quantities is composed of the square of the first, plus twice the product of...first by the second, plus the square of the second. Thus, to form the square of 5a3+8a3i, we have, from what has just been said, 2d. To form the square...
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Elements of Algebra

Algebra - 1838 - 372 pages
...to form the square or second power of the binomial, (a+*)- We have, from known principles, That is, the square of the sum of two quantities is equal to...first by the second, plus the square of the second. Thus, to form the square of 5a"-\-8a2b, we have, from what has just been said, 2d. To form the square...
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First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - Algebra - 1839 - 264 pages
...to form the square or second power of the binomiaj (a+b). We have, from known principles, That is, the square of the sum of two quantities is equal to...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 = 4<z3 + 12ab + 962. 2. (5a6 + 3<zc)2...
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Elements of Algebra

Algebra - 1839 - 368 pages
...is, the square of the difference between 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. Thus, (7o3i3— 12ai3)3=49o4i4— 168a3i5+144a3i6. 3d. Let it be required to multiply a-\-b by a —...
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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...first by the second, plus the square of the second. Thus, to form the square of 5o 2 +8a 2 i, we have, from what has just been said, (5a 2 + 8a 2 i) 2...
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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1842 - 284 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...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. 3. (5a6+3ac)2 =25a262+...
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Elements of Algebra: Including Sturms' Theorem

Charles Davies - Algebra - 1845 - 382 pages
...rules for the multiplication of algebraic quantities in the demonstration of the following theorems. THEOREM I. The square of the sum of two quantities...first by the second, plus the square of the second. Let a denote one of the quantities and l1 the other: then a + b — their sum. Now, we have from known...
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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...first by the second, plus the square of the second. 17. Multiply a — b by a — b. The product is a2 — 2a6+62 ; from which we perceive, that the square...
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