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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, in theory and practice

James William M'Gauley - 1854 - 284 pages
...algebraic formula [sec. 1, 1], — For, the result of the multiplication may be read as follows : — " the square of the sum of two quantities is equal to...the sum of their squares, plus twice their product." And as the given quantities may represent any possible ones, the formula is general. 36. EXAMPLE 2...
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A treatise on the elements of algebra, by G. Ainsworth and J. Yeats

G. Ainsworth - 1854 - 216 pages
...difference of their squares. II. (a + b}*=a? + 2ab + b2 ; that is, The square of the sum of two numbers is equal to the sum of their squares, plus twice their product. III. (a— b)2=ai— Zab + b2 ; that is, The square of the difference of two numbers is equal to the...
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Annual Report and Documents, Volumes 35-42

New York (State) School for the deaf, White Plains - 1854 - 936 pages
...gives minus." (b-— 1)=! (If— 1)=(&6— &s)." What is the square of the sum of two quantities T " 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 - 1855 - 356 pages
...Ex. 2. Required the square of 3+2 v/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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The Elements of Algebra

Elias Loomis - Algebra - 1856 - 280 pages
...theorems are of such extensive application that they should be carefully committed to memory. THEOREM I. The square of the sum of two quantities is equal to the square of the first, plus twice the product oj the first by the second, plus the square of the second....
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Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

Joseph Ray - Algebra - 1857 - 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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Algebra for High Schools and Colleges: Containing a Systematic Exposition ...

James B. Dodd - Algebra - 1859 - 368 pages
...of (a+x) (a— a) 1 What is the Product of (a+5) (a— 5) 1 Of (3+y) (3— y)1 Of (x— 1) (a (59.) The Square of the sum of two quantities is equal to the sum of the squares plus twice the product of the two quantities. Thus (a+b) (a+b), that is, the square of...
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The University Algebra ...

John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...+ Зааг* —х". .dnę. a'— 2ax+x\ CHAPTER III. THEOREMS AND FACTORING. 0 THEOREM I. ( 1 09.) 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 Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1859 - 422 pages
...certain cases in Multiplication of frequent occurrence, and should be carefully learned. 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 and second, plus the square of the second....
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1860 - 412 pages
...+ b) X (a + b), or performing the multiplication indicated, (a + b)z = <£• + 2ab + 62 ; 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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