 | 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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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. 
