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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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New Elementary Algebra

Benjamin Greenleaf - 1870 - 336 pages
...operations. THEOREM I. 76. The square of the sum of two quantities is equal to the square of the firsl, plus twice the product of the first by the second, plus the square of the second. For, let a represent one of the quantities, and b the other; then, (a + ft) = (a + ft) X (a + 6)...
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Elements of Algebra: For Colleges, Schools and Private Students

Joseph Ray - Algebra - 1866 - 420 pages
...truths. The following theorems serve to show some of its most simple applications. 78. Theorem I. — The square of the sum of two quantities is equal to...first by the second, plus the square of the second. Let a represent one of the quantities, and ba +6 the other. a +6 Then,a+6=theirsum;and(a+6)X(a+6),...
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New Higher Algebra: An Analytical Course Designed for High Schools ...

Benjamin Greenleaf - Algebra - 1871 - 412 pages
...That is, The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second. Also, (a _|- 5) (a — 5) = a2 — 52. (3) That is, jTAe product of the sum and difference of two quantities...
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Arithmetic and Its Applications ...

Dana Pond Colburn - 1871 - 392 pages
...the second; Tlir filчаге of flie sum of antf tico numbers equals the square of the first, plui twice the product of the first by the second, plus the square of the tecond. Illustrations. (7 + 5)== 7= + 2 X 7 X 5 + 52 = 49 + 70 + 25 = 144= 12' (8 + 4)2 = 82 + 2...
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Elementary Algegra

Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...and, in some instances, by abridged methods derived from the following theorems : Tfieorem I. 113. The square of the sum of two quantities is equal to...first by the second, plus the square of the second, For, let a and 6 represent two quantities, then a + b will denote their sum, and (a + b)2 = (a + 6)...
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The Art of Computation, Designed to Teach Practical Methods of Reckoning ...

David White Goodrich - Ready-reckoners - 1873 - 220 pages
...are 400, 900, 1600, 2500, etc. Now since -(a+b)*=a'+2ab.+ b', the square of the sum of two numbers is equal to the square of the first, plus twice the...first by the second, plus the square of the second. Thus 212 = 20'+ 2(20+ 1) + 1 = 400+40+ 1 = 441. So 105* — 10000+ 1000+25 = 1 1025. 85'= 6400+ 800+25=...
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A Treatise on Algebra

Elias Loomis - Algebra - 1873 - 396 pages
...The three following theorems have very important applications. The square of the sum of two numbers is equal to the square of the first, plus twice the...first by the second, plus the square of the second. Thus, if we multiply a+b by a+b a?+ ab we obtain the product az+2ab+b2. of the result, without the...
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New Higher Algebra: An Analytical Course Designed for High Schools ...

Benjamin Greenleaf - 1873 - 420 pages
...a2 + 2ab + 2. (1) That is, The square of the sum of two quantities is equal to the square nf tlie first, plus twice the product of the first by the second, plus the square of the second. Again, (a — )2 = (a — b) (a — ) = a2 — 2a + J2. (2) That is, Also, (a + b) (a — b)...
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A Practical Business Arithmetic ...

Lorenzo Fairbanks - 1875 - 468 pages
...Binomial is a quantity consisting of two terms, and its square is equal to the square of the first term, plus twice the product of the first by the second, plus the square of the second. Let 35 be written 30 + 5. Then, squaring this number, by multiplying each part separately, we hare,...
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New Elementary Algebra: In which the First Principles of Analysis are ...

Benjamin Greenleaf - Algebra - 1877 - 662 pages
...following theorems give rise to formulas, useful in abridging algebraic operations. THEOREM I. 76. The square of the sum of two quantities is equal to...twice the product of the first by the second, plus tlte square of the second. For, let a represent one of the quantities, and i the other ; then, (...
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