| William Emerson - Algebra - 1780 - 531 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 - 303 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... | |
| Jeremiah Day - Algebra - 1820 - 332 pages
...by applying the principle, that the product of the sum and diifereuce of two quantities, is eqiinl **to the difference of their squares. (Art. 235.) The...the sign which connects the terms is changed from** + to — , or from — to +, will be the factor required. Thus (v/a+y&)x(V«-V&)= V«2— Sl2=ab, which... | |
| Edward Riddle - 1824
....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... | |
| Industrial arts - 1830
...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 - 1831 - 332 pages
...into a binomial surd containing only the square root, may be found by applying the principle, that **the product of the sum and difference of two quantities,...the sign which connects the terms is changed from** -\-to-, or from -to +, will be the factor required. Thus (Va+y6) X (V a - Vfr) = V« 2 - A/6 2 =a -... | |
| Jeremiah Day - Algebra - 1832 - 332 pages
...into a binomial surd containing only the square root, may be found by applying the principle, that **the product of the sum and difference of two quantities,...-, or from -to +, will be the factor required. Thus** (Va+V6) X (Va - V6) = Vas - A/6*=a - b, which is free from radicals. And (3 - 2V2) X (3+2V2) = 1When... | |
| Jeremiah Day - Algebra - 1832 - 332 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... | |
| Olinthus Gregory - 1833 - 427 pages
...is equal to the sum of the squares of the two quantities together with twice their product 2. That **the product of the sum and difference of two quantities is equal to the difference of their squares.** 3. That the cube of the binomial a + b, is a* + 3 a* b + 3 a b3 + b3. SECTION IV. — Division. 1.... | |
| William Smyth - Algebra - 1833 - 280 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... | |
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