| Charles Davies - Algebra - 1842 - 284 pages
...a— b, we have (a—b)2 = (a—b) (a—b)—az~2ab+bz. That is, the square of the difference between **two quantities is equal to the square of the first,...first by the second, plus the square of the second,** 1. Form the square of 2a— b. We have (2a—6)2=4o2—4a6+62. 2. Form the square of 4ac—bc. We have... | |
| Charles Davies - Algebra - 1842 - 368 pages
...difference, a—b, we have (a—b)2=(ab) (ai)=a 2 —2ai+i2: That is, the square of the difference between **two quantities is equal to the square of the first,...first by the second, plus the square of the second.** Thus, (7o 2 i2—12ai 3 ) 2 =49a 4 i 4 —168a 3 i 6 +144a 2 i 6 . 3d. Let it be required to multiply... | |
| Ormsby MacKnight Mitchel - Algebra - 1845 - 308 pages
...second. 17. Multiply a — b by a — b. The product is a2 — 2a6+62 ; from which we perceive, that the **square of the difference of two quantities, is equal...first by the second, plus the square of the second.** 18. Multiply a+b by a — b. The product is a2 — b2 ; whence we find, that the product of the sum,... | |
| Charles Davies - Algebra - 1845 - 382 pages
...36a862 + 108a5ft* + 81a2ft6 ; also, (8a3 + 7acb)2-. THEOREM II. The square of the difference between **two quantities is equal to the square of the first, minus twice the product of the first by the** tecond, plus the square of the second. Let a represent one of the quantities and b the other : then... | |
| Elias Loomis - Algebra - 1846 - 376 pages
...common mistakes of beginners is to call the square of а + b equal to a2 + 62. THEOREM II. (61.) The **square of the difference of two quantities, is equal...of the first, minus twice the product of the first** and second, plus the square of the second. Thus if we multiply a — b By a — b We obtain the product... | |
| Elias Loomis - Algebra - 1846 - 380 pages
...common mistakes of beginners is to call the square of o + b equal to a2 + 62. THEOREM II. (61.) The **square of the. difference of two quantities, is equal...of the first, minus twice the product of the first** and second, plus the square of the second. Thus if we multiply a — b By a — b a2—ab — ab We... | |
| Algebra - 1847 - 408 pages
...36a»62 + 108a56* + 8 la2*6 ; also, (8a3 + 7ac6)2=. THEOREM II. The square of the difference between **two quantities is equal to the square of the first,...first by the second, plus the square of the second.** Let a represent one of the quantities and b the other : then a — b = their difference. Now, we have... | |
| Algebra - 1847 - 386 pages
...THEOREM II. The square of the difference between two quantities is equal to the square of the ßrst, **minus twice the product of the first by the second, plus the square of the second.** Let a represent one of the quantities and b the other : then a — b = their difference. Now, we have... | |
| Joseph Ray - Algebra - 1848 - 250 pages
...a— b a2 — ab —a6+6' 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...first by the second, plus the square of the second.** EXAMPLES. 1 (5— 4)2=25— 40+16=1. 2. (2a— 6)2=4a2-4a6+62. 3. (3x- 22/)2=9x2-12xy+4y2. 4. (^-y2)s=x4-2xy+/.... | |
| Charles Davies - Algebra - 1848 - 300 pages
...39. To form the square of a difference a — b, we have That is, the square of the difference between **two quantities is equal to the square of the first,...first by the second, plus the square of the second.** 1. Form the square of 2a — b. We have (2<z — i)2 = 4a2 — 2. Form the square of 4<zc— be. We... | |
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