 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.  A Treatise on Algebra - Pàgina 28per Elias Loomis - 1855 - 316 pàginesVisualització completa - Sobre aquest llibre
 | Charles Davies - 1866 - 314 pàgines
...(a - b) (a- b) = a2- 2ab + P. That is, The square of the difference of any two quantities is eq^^al to the square of the first, minus twice the product of the first by the second, plus the square of the second. 1. Find the square of 2a — b. We have, (2a — b)2... | |
 | Horatio Nelson Robinson - 1868 - 430 pàgines
...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...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 the sum and... | |
 | William Frothingham Bradbury - 1868 - 264 pàgines
...+ 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 - 1868 - 312 pàgines
...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 - 1868 - 386 pàgines
...(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 pàgines
...Iheorem for finding the square of the difference of any two quantities is deduced. THEOREM II. — 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. EXAMPLES. 1. 2. 3. 4. 5. **. 'J — ~4f — "g Y~TTn... | |
 | Joseph Ray - 1866 - 420 pàgines
...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...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 — 6... | |
 | Benjamin Greenleaf - 1871 - 412 pàgines
...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 - 1871 - 244 pàgines
...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 - 1873 - 268 pàgines
...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...the first and second, plus the square of the second. a — b PROOF. Let a and b stand for any a — b two quantities. Then, multiplying a ^ ^~ — b by... | |
| |
