 | William Emerson - 1780 - 574 sider
...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 - 1814 - 304 sider
...• ' 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 - 1820 - 352 sider
...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 - 572 sider
....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... | |
 | 1830 - 482 sider
...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 - 1831 - 358 sider
...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 - 1832 - 360 sider
...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 - 1832 - 354 sider
...!/" ' 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 - 1833 - 288 sider
...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 sider
...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... | |
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... 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. 
