 | Benjamin Greenleaf - 1870 - 334 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)... | |
 | 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),... | |
 | 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... | |
 | 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... | |
 | 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)... | |
 | 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=... | |
 | 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... | |
 | 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)... | |
 | Lorenzo Fairbanks - 1875 - 472 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,... | |
 | 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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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. 
