 | William Emerson - 1780 - 574 Seiten
...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 Seiten
...• ' 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 - 1824 - 572 Seiten
....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 - 1827 - 352 Seiten
...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 —... | |
 | 1830 - 482 Seiten
...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 - 1832 - 354 Seiten
...!/" ' 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 Seiten
...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 Seiten
...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 - 1834 - 472 Seiten
...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... | |
 | Robert Mudie - 1836 - 524 Seiten
...-b —ab—b2 a2— 62 Here — b changes the signs in the second line of the product, and +ab — a 6 is =0, and may be left out in adding. Hence we...principle : — the product of the sum and difference nf two quantities is equal to the difference of their squares. If we subtract the square of a — b... | |
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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. 
