| Benjamin Greenleaf - 1863 - 338 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...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)2 = (a -f- 6) X (a + 6)... | |
| Charles Auguste A. Briot - 1863 - 376 pages
...SUM OF TWO NUMBERS. 156. The square of the sum of two numbers equals the square of the first number, **plus twice the product of the first by the second, plus the square of the second.** Be it given to raise the sum of 7 + 5 to the square ; it is necessary to multiply 7 + 5 by 7 + 5. In... | |
| Gerardus Beekman Docharty - Algebra - 1862 - 338 pages
...THEOREM II. 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** (he second. EXAMPLES. 2. (3x-2a)'=(3x-2a)(3x-2a). Ans. 3. (9x-3y)'= Ans. 4. (6-i)'= Ans. 5. (Gt)'=... | |
| Joseph Ray - Algebra - 1866 - 252 pages
...a2+2a6-j-62. Thus: a+6 a+6 a2+2a6-|-62 But a+6 is the sum of the quantities, a and 6. Hence, Theorem I. — **The square of the sum of two quantities is equal to...first by the second, plus the square of the second.** NOTE . — Let the pupil apply the theorem by writing the following examp\>, enunciated thus : What... | |
| Benjamin Greenleaf - 1866 - 336 pages
...algebraic operations. THEOREM I. 76, The square of the sum of two quantities is equal to the tquare **of the first, 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 + 6)' = (a + 6) X (a + V) = a3... | |
| Joseph Ray - Algebra - 1852 - 420 pages
...THEOREM II. — 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** se'vnd. Let a represent one of the quantities, and b the other ; then a — 6=their difference ; and... | |
| Joseph Ray - Algebra - 1866 - 252 pages
...square of the difference of two quantities is equal to the square of the first, minus twice the prodnet **of the first by the second, plus the square of the second. 1.** (5— 4)2=25— 40+16=1. 2'. (2a— 6)2=4a2— 3. (3a!— 2yy=9x*-— 4. (x*— y*y=tf 5. (ax— *-)2=aV—... | |
| Charles Davies - Algebra - 1867 - 320 pages
...6) = a2 + 2a5 f- b\ That is, The square &f the sum of two quantities is equal to the tqitart •)f **the first, plus twice the product of the first by the second,** plat the square of the second. 1. Form the square of 2a + 36. We have from the rule (2a + 36)2 = 4a2... | |
| Elias Loomis - Algebra - 1868 - 386 pages
...2 = 10. 67. The square of the difference of two numbers is equal to the square of the first, minus **twice the product of the first by the second, plus the square of the second.** Thus, if we multiply a— b by a—b a 2 — ab - ab+b* we obtain the product a 2 —2ab+b 2 . EXAMPLES.... | |
| Robert Wallace - 1870 - 164 pages
...following theorem for finding the square of the sum of a,ny two quantities is deduced. THEOREM I. — **The square of the sum of two quantities is equal to...first by the second, plus the square of the second.** EXAMPLES. 1. 2. 3. 4. 5. 0. 2oa;+4a2. Ans. Ans. Ans. Ans. „. 6+J)2=36--3+,4i7=39TIcT. Ane. 24. Multiply... | |
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