... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares. The Elements of Algebra - Page 76by Elias Loomis - 1856 - 268 pagesFull view - About this book
| William Emerson - Algebra - 1780 - 574 pages
...ss 4- iid + dd 4 ss — <isd + dd and Lb ~ 4 and AA— EE = ±^ = sd. 4 Cor. "The produff of the fum **and difference of two quantities^ is equal to the difference of their** fquares. PROBLEM LXVIII. *Two quantities being given to find the fquare of the fum. Let a be the greater... | |
| Jeremiah Day - Algebra - 1814 - 304 pages
...• ' 6. j 235. If a+b be multiplied into a— b, the product will be «*— 6a: (Art. 110.) that is, **The product of the sum and difference of two quantities, is equal to the difference of their squares.** This is another instance of the facility with which general truth are demonstrated in -algebra- See... | |
| Edward Riddle - Nautical astronomy - 1824 - 572 pages
....sin A— B=;gin A . cosB + cos A . sinB. sin A . cos В — cos A . sin B. And as the rectangle, or **the product, of the sum and difference of two quantities, is equal to the difference of their squares** } sin A . cos В + cos A . sin В . sin A . cos В «- ços A • ein В, is equal мл — cot2A 1... | |
| Jeremiah Day - Algebra - 1827 - 352 pages
...multiplied into a binomial surd containing only the squre root, may be found by applying the principle, fhat **the product of the sum and difference of two quantities, is equal to, the difference of their squares.** (Art. 235.) The binomial itself, after the sign which connects the terms is changed from -f to —... | |
| Industrial arts - 1830 - 482 pages
...the right angle ; let AC= 100000000000 1, AB:=999999999999. Now, since the rectangle under the sure **and difference of two quantities is equal to the difference of their squares** .'. (AC+AB) • (AC-AB) = AC2 - AB2 = BC2 = 2000000000000 x 2 = 4(100000000000 .'. BC = */ 4000000000000... | |
| Jeremiah Day - Algebra - 1832 - 354 pages
...!/" ' ya y"!/"" 3. -a-3xo~3=-a~6. 4. fl-3xrf=rf~'2=<P. 5. a -nx o'"=a"'~"• 6. «-8 THE PRODUCT OP **THE SUM AND DIFFERENCE OF TWO QUANTITIES, IS EQUAL TO THE DIFFERENCE OF THEIR SQUARES.** This is another instance of the facility with which general truths are demonstrated in algebra. See... | |
| William Smyth - Algebra - 1833 - 288 pages
...quantity, minus the double product of the first by the second, plus the second power of the second. 6. **The product of the sum and difference of two quantities is equal to the difference of their** second powers. SECTION V. — ALGEBRAIC FRACTIONS. 55. When the division of two algebraic quantities... | |
| Ireland commissioners of nat. educ - 1834 - 370 pages
...truth of this rule is evident from 47. I. and from Cor. S. II., which says, that the rectangle under **the sum and difference of two quantities is equal to the difference of their squares.** 3. Given AB : 5, B С 4 ; required AC : 52 — 4* = 9 ; then V 9 = 3 the side A С ; or (5 + 4) X (5... | |
| Olinthus Gregory - Mathematics - 1834 - 472 pages
...squares of the two quantities together with twice their product 2. That the product of the sum arid **difference of two quantities is equal to the difference of their squares.** 3. That the cube of the binomial a + b, is a3 + 3 a* b + 3 ab* + 0s. SECTION IV. — Division. 1. To... | |
| Silas Totten - Algebra - 1836 - 360 pages
...place of a and b, it follows, that this property is general. This property may be thus enunciated : — **The product of the sum and difference of two quantities is equal to the difference of their squares.** Having demonstrated this property, we can make use of il to shorten the operation of multiplication... | |
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