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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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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 of...
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A New Introduction to the Science of Algebra ...

Silas Totten - Algebra - 1836 - 320 pages
...4a6a) x (7asb + 4a62) = 49aź6s — 16а╗ЬЧ The following properties are also of great use : — 1. The square of the sum of two quantities, is equal...the sum of their squares plus twice their product. Let a and b be the quantities, then a -fb is theipsum, and we have, . . This property admits of like...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - Mathematics - 1836 - 542 pages
...general expression, or by numbers for any given particular case. Therefore, we may state generally, that the square of the sum of two quantities is equal to four times the product of the quantities, together with the square of their difference. Thus if a is...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - Mathematics - 1836 - 524 pages
...general expression, or by numbers for any given particular case. Therefore, we may state generally, that the square of the sum of two quantities is equal to four times the product of the quantities, together with th"e square of their difference. Thus if a...
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The British Cyclopaedia of the Arts, Sciences, History, Geography ...

Charles Frederick Partington - Encyclopedias and dictionaries - 1838 - 1116 pages
...them 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...
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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 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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The elements of algebra

Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...by a+╗(31.) 2. Find the square of a — x (179.) It appears from these two examples that — 1The square of the sum of two quantities is equal to the sum of the squares of these quantities and twice their product; and, The square of the difference of two quantities...
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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 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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First Lessons in Algebra: Being an Easy Introduction to that Science ...

Ebenezer Bailey - Algebra - 1840 - 270 pages
...20, and b — 8 ; then a + b = 28. a + b ab a2 + ab + ab + Hence it appears, that the second power of the sum of two quantities is equal to the sum of their second powers, increased by twice their product. 19. What is the second power of a — b 1 a — I,...
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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 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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