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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 by the second, plus the square of the second. "
A Short Course in Higher Algebra: For Academies, High Schools, and Colleges - Page 44
by Webster Wells - 1889 - 426 pages
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A Treatise on Algebra

George Peacock - Algebra - 1830 - 732 pages
...other. This is the square of a + b (Art. 11), and the result may be expressed in words, as follows : " The square of the sum of two quantities is equal to the sum of the squares of the two quantities, together with twice their product.1"* (2) To find the square...
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A New Introduction to the Science of Algebra ...

Silas Totten - Algebra - 1836 - 320 pages
...4a6a) x (7asb + 4a62) = 49a«6s — 16а»ЬЧ The following properties are also of great use : — 1. The square of the sum of two quantities, is equal to the sum of their squares plus twice their product. Let a and b be the quantities, then a -fb is theipsum,...
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Elements of Algebra

Algebra - 1838 - 372 pages
...required 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...square of the first, plus twice the product of the first by the second, plus the square of the second. Thus, to form the square of 5a"-\-8a2b, we have,...
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The British Cyclopaedia of the Arts, Sciences, History, Geography ...

Charles Frederick Partington - Encyclopedias and dictionaries - 1838 - 1116 pages
...will be useful exercises. It is required to prove 1°. That (a + 6) (n + b) = os + lab + 63 ; or, that the square of the sum of two quantities is equal to the square of the first quantity, plus the square of the second, plus twice the product of the first and second. 2°. That...
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First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - Algebra - 1839 - 264 pages
...required 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...square of 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...
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Elements of Algebra

Bourdon (M., Louis Pierre Marie) - Algebra - 1839 - 368 pages
...or second power of the binomial, (a-\-b). We have, from known principles, That is, the square ofthe sum of two quantities is equal to the square of the first, plus twice the product of tl>e first by the second, plus the square of the second. Thus, to form the square of 5a2+8a26, we have,...
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Elements of Algebra

Charles Davies - Algebra - 1842 - 368 pages
...power of 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...square of the first, plus twice the product of the first by the second, plus the square of the second. Thus, to form the square of 5o 2 +8a 2 i, we have,...
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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1842 - 284 pages
...required 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...square of 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...
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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...square of the first plus twice the product of the first by the second, plus the square of the second. 17. Multiply a — b by a — b. The product is...
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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...square of the first, plus twice the product of the first by the second, plus the square of the second. Let a denote one of the quantities and l1 the other:...
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