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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. "
Elementary Algebra: Embracing the First Principles of the Science - Page 25
by Charles Davies - 1842 - 258 pages
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Algebra for Schools and Colleges

William Freeland - Algebra - 1895 - 328 pages
...+ 1). 61. The three following theorems are useful in the multiplication of binomials. That is : 62. The square of the sum of two quantities is equal to...first by the second, plus the square of the second. II. (а-b)2 = а2That is : 63. The square of the difference of two quantities is equal to the square...
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Concrete Geometry for Beginners

Adelia Roberts Hornbrook - Geometry - 1895 - 222 pages
...there in the rectangle DGHE? How many in all ? PRINCIPLE 51. — The square of the sum of two lines is equal to the square of the first plus twice the...first by the second plus the square of the second. 29. Draw the square of the sum of two lines, one 5 inches, the other 3 inches, and show the truth of...
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Robinson's New Higher Arithmetic: For High Schools, Academies, and ...

Horatio Nelson Robinson - Arithmetic - 1895 - 526 pages
...right. Since the square of a number divided into any two parts is equal to the square of the first part, plus twice the product of the first by the second, plus the square of the second part ( 734), having found the square of the first part, which is 4iH)0, the remainder 517 must be...
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Transactions of the National Eclectic Medical Association of the ..., Volume 24

National Eclectic Medical Association of the United States of America - 1897 - 382 pages
...times, as expressed by the multiplier. In algebra, the square of the sum- of two quantities is exactly equal to the square of the first, plus twice the product...first by the second, plus the square of the second. In geometry, the square of the hypothenuse of a right-angled triangle exactly equals the sum of the...
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A School Algebra Complete

Fletcher Durell, Edward Rutledge Robbins - Algebra - 1897 - 478 pages
...b'', which, stated in general language, is the rule— The square of the sum of two quantities equals the square of the first, plus twice the product of...first by the second-, plus the -square of the second. Ex. (2z + ЗуУ = 4з? + 2xy + Qf, Product. Since the square of 2x is 4z2, twice the product of...
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The Elements of Mechanical Engineering, Volume 1

International Correspondence Schools - Electrical engineering - 1897 - 672 pages
...quantities, the square of tlie sum of tii'o quantities equals the square of the first, plus tiuice the product of the first by the second, plus the square of the second. 429. Also, that The square of the difference of two quantities equals the square of the first, minus...
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Arithmetic, algebra, logarithms, geometry and trigonometry, elementary ...

International Correspondence Schools - Civil engineering - 1899 - 722 pages
...429. Also, that The square of the difference of two quantities equals the tquare of the first, minus twice the product of the first by the second, plus the square of the second. 430. The third, example is: 3. To find the product of the sum and difference of two quantities. By...
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College Algebra

James Harrington Boyd - Algebra - 1901 - 816 pages
...Theorem III, is the fraction itself. 402. THEOREM V. — The square of the sum of two quantities is the square of the first plus twice the product of...first by the second plus the square of the second. By multiplying a -(- b by itself it is found that (a -\- b)* = (a+b) (а + b) = o2+ 2 ab + b\ Thus...
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College Algebra

James Harrington Boyd - Algebra - 1901 - 818 pages
...THEOREM V. — The square of the sum of two quantities is the square of the first plus twice, tlie product of the first by the second plus the square of the second. By multiplying a + I by itself it is found that (a + I,)* = (a+ I,) (a + 1) = a-+ 2 ab + a. Thus...
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The Model Algebra: Arranged for Elementary Schools

Edward Gideon - Arithmetic - 1903 - 166 pages
...which is the difference of the two quantities, and the other is the square of the first quantity, plus the product of the first by the second, plus the square of the second quantity. EXAMPLES. 161. a3 + 6'. 171. aV + 1. 181. 8a3 - 6V. 162. ж3 + z2. 172. 1 -6V. 182. a3 +...
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