 | Horatio Nelson Robinson - 1868 - 430 pages
...second, plus the square of the second. II. (a— l)'=(a— ¿) (a— i) = a'— ïab+V Or, in words, The square of the difference of two quantities is...of the first, minus twice the product of the first and second, phis the square of the second. III. (a+l) (a_b)=a«_ £,' Or, in words, The product of... | |
 | William Frothingham Bradbury - Algebra - 1868 - 264 pages
...+ y2. 2. 2x + 2y. Ans. 4 a;2 3. x+ 1. 4. 4 + a;. 5. 2x + 3y. Ans. 4z2-f6. 3a + 6. THEOREM III. 59. The square of the difference of two quantities is...square of the first, minus twice the product of the two, plus the square of the second. Let a and 6 represent the two quantities, and a ]> 6 ; their difference... | |
 | Elias Loomis - Algebra - 1868 - 312 pages
...the most common mistakes of beginners is to call the square of a+b equal to a'+b'. THEOREM II. (66.) The square of the difference of two quantities is equal to the square of the first, minus twice theprod~ net of the first and second, plus the square of the second. Thus, if we multiply a —b by... | |
 | Elias Loomis - Algebra - 1868 - 386 pages
...(5a+3Z>) 2 = 8. 4. (5a 2 +2&) 2 ^ 9. 5. (5a*+b) 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*... | |
 | Robert Wallace - 1870 - 164 pages
...example, the following Iheorem for finding the square of the difference of any two quantities is deduced. THEOREM II. — The square of the difference of two...of the first, minus twice the product of the first by the second, plus the square of the second. EXAMPLES. 1. 2. 3. 4. 5. **. 'J — ~4f — "g Y~TTn... | |
 | 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...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... | |
 | 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... | |
 | Joseph W. Wilson - Algebra - 1873 - 268 pages
...Then, 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...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 quantities.... | |
 | 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...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, then... | |
 | 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...square of the first, minus twice the product of the two, plus the square of the second. 87. THEO. — The product of the sum and difference of two quantities... | |
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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. 
