 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...operations, the results which follow: I. (a+b)'=(a+u) (a+b')=a>+2ab+bt Or, expressing the result in words, The square of the sum of two quantities is equal to...of the first, plus twice the product of the first and second, plus the square of the second. II. (a— b)'=(a— ¿) (a— b)=a'— 2ab+b* Or, in words,... | |
 | Charles Auguste A. Briot - 1863 - 374 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 - 336 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)'=... | |
 | Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...operations, the results which foltow: Or, expressing the result in words, The square of the sum of tico quantities is equal to the square of the first, plus twice the product of the first -and second, plus the square of the second. . • II. (a— b)'=(a— u) (a— b) = at— 2ab+b' Or,... | |
 | Paul Allen Towne - Algebra - 1865 - 314 pages
...4, and a; + 7 by a; — 4. 62. Since (x + y) (x + y) = (x + y)3 = x3 + 2xy + y3,it follows th at J%e square of the sum of two quantities is equal to the square of the jirst + twice their product + the square of the last. EXAMPLES. 1. (a + 6)3 = a2 + 2a6 + 43. 2. (2a... | |
 | Joseph Ray - Algebra - 1866 - 250 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... | |
 | Education - 1866 - 538 pages
...on their way." After careful thought and research, we come fully to comprehend the truth that •' the square of the sum of two quantities is equal to...square of the first, plus twice the product of the two, plus the square of the second" ; and when the tyro in Algebra jabbers off this formula, we vainly... | |
 | John Fair Stoddard, William Downs Henkle - Algebra - 1866 - 546 pages
...10aV+5o«4— if by a1— Sa'x + Sox1 «. a1— CHAPTER III. THEOKEMS AND FACTORING. THEOREM I. . (1O9.) The square of the sum of two quantities is equal to the square of the fast, plus twice the product of tke first ky tlte second, plus the square of the second. DEMONSTRATION.... | |
 | Joseph Ray - Algebra - 1852 - 422 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—... | |
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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. 
