 | Paul Allen Towne - Algebra - 1865 - 314 pages
...numerical value when a; = 8, y = 8. 63. Since (*— y) ( x -y) = (x — yf = x'-2xy+y3, it follows that The square of the difference of two quantities is equal to the square of the first — twice their product -\- the square of the last. EXAMPLES. 1. (« — 6)" = ^ — 2a6 + 62. 2. (2a... | |
 | Joseph Ray - Algebra - 1866 - 420 pages
...theorem. APPLICATION. 1. (2+5)2=4+20+25=49. 3. (ax+by)*=ax* -\-2abxy -\-by*. 4. ' 79. Theorem II. — The square of the difference of two quantities is...of the first, minus twice the product of the first ly the second, plus the square of the second. Let a represent one of the quantities, and 6 a — 6... | |
 | Benjamin Greenleaf - 1866 - 336 pages
...+ 4 a4 ô2. 4. Square a3 b2 + 3 a2 a3 c4. Ans. a6 54 + 6 a5 55 c4 + 9 a4 #> c3. THEOREM II. 77t 7%e square of the difference of two quantities is equal...square of the first, minus twice the product of the firsl by the second, plus the square of the second. For, let a represent one of the quantities, and... | |
 | Joseph Ray - Algebra - 1866 - 250 pages
...a?—ab a2— 2a6-|-62 But a — b is the difference of the quantities, a and 6. Hence, ! Theorem II. — The square of the difference of two quantities is equal to the square of the first, minus twice the prodvet of the first by the second, phis the square of the second. 1. (5— 4)2=25— 40+16=1. 2. (2a—... | |
 | Joseph Ray - Algebra - 1866 - 252 pages
...a&+62 a?— 2a6+62 But a — b is the difference of the quantities, a and' 6. Hence, Theorem II. — The 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'.... | |
 | Charles Davies - Algebra - 1867 - 322 pages
...(a — 6)2 = (a — 6) (a — 6) = a2 — 2a6 + 62 : Thaf. is, The square of the difference between two quantities is equal to the square of the first, minus twice the product of the first by 1h* second, plus the square of the second. 1. Form the square of 2a — b. We have (2o- 6)2 = 4a2 -... | |
 | 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... | |
 | 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... | |
| |
The square of the difference of 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. Thus, (a — 6)* = (a — b) (a — 6)=a2— 2a6 + 6'. 
