| 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)... | |
| 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 - 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,... | |
| 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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