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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 Complete Course in Algebra for Academies and High Schools - Side 42
av Webster Wells - 1885 - 349 sider
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A Treatise on Algebra

George Peacock - 1830 - 732 sider
...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 - 1836 - 320 sider
...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

1838 - 372 sider
...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 - 1838 - 1116 sider
...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 - 1839 - 264 sider
...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) - 1839 - 368 sider
...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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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - 1842 - 284 sider
...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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Elements of Algebra

Charles Davies - 1842 - 368 sider
...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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An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - 1845 - 308 sider
...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 - 1845 - 382 sider
...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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