 | Benjamin Greenleaf - Algebra - 1871 - 412 pages
...the square of the second. _ Again, (a — by = (a — 5) (a — 5) = a2 — 2a6 + 52. (2) That is, The square of the difference of two quantities is...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... | |
 | Joseph Ray - Algebra - 1866 - 420 pages
...a2+2afi+&2 the theorem. APPLICATION. 1. (2+5)2=4+20+25=49. 2. (2m+3n)2=4m2-f I2wm+9n2. 79. Theorem II. — The square of the difference of two quantities is...square of the first, minus twice the product of the first by the second, plus the square of the second. Let a represent one of the quantities, and 6 a... | |
 | James Haddon - Algebra - 1871 - 244 pages
...of two quantities is equal to the и«.'» of their squares, together with twice their product. 2. The square of the difference of two quantities is equal to ' the sum of their squares, diminished by twice their product. 3. The product of the sum and difference of... | |
 | Edward Olney - Algebra - 1873 - 354 pages
...square of the first, plus twice the product of the two, plus the square of the second. 86. THEO. — The square of the difference of two quantities is...product of the two, plus the square of the second. 87. THEO. — The product of the sum and difference of two quantities is equal to the difference of... | |
 | Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...4. What is the square of c + 3 ? 5. What is the square of 3 + a*? Ans. 9+6ai + at. Theorem, II. 114. The square of the difference of two quantities is...square of the first, minus twice the product of the first by the second, plus the square of the second. • For, let a and b represent the two quantities,... | |
 | Joseph W. Wilson - Algebra - 1873 - 268 pages
...multiplying a fl2 , ^~ + b by itself, we have what the theorem ' ab + V states. as + 2 ab + b2 Theorem II. The square of the difference of two quantities is...square of the first, minus twice the product of the first and second, plus the square of the second. a — b PROOF. Let a and b stand for any a — b two... | |
 | Elias Loomis - Algebra - 1873 - 396 pages
...(5a3+8a26)2= 3. (5a+36)2= 8. 4. (5a2+ 26)2= 9. 5. 5a3+i= 10. 67. T/ie square of the difference of two numbers is equal to the square of the first, minus twice the product of the first by the sec~ and, plus the square of the second. Thus, if we multiply a— 6 by a— b a?— ab... | |
 | William Frothingham Bradbury - 1875 - 280 pages
...2y. Ans. 4 ж2 3. x + 1. 4. 4 + ж. 5. 2ж + 3у. Ans. 4зг'4 6. 3а + 6. THEOREM III. 59, ГЛе square of the difference of two quantities is equal...second. Let a and 6 represent the two quantities, and а ]> b ; their di/ ference will be а — 6. PROOF. a —b a —b a? — а 5 — ab + b3 According... | |
 | Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...and second, plus the square of the second. II. (a — b)*=(a—b)(a — b) = a*—2ab + & ; hence, The square of the difference of two quantities is...square of the first, minus twice the product of the first and second, plus the square of the second. III. (a +b)(a — b)—a*-^; hence, Tue product of... | |
 | William Guy Peck - Algebra - 1875 - 348 pages
....product of the first and second, plus the square of the second. 2°. The square of the difference of any two quantities, is equal to the square of the first, minus twice the product of the first and second, plus the square of the second. 3°. The product of the sum and difference of any... | |
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... the square of the second. In the second case, we have (a — &)2 = a2 — 2 ab + b2. (2) That is, the square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second. 
