... 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. A Treatise on Algebra ... - Page 100by William Smyth - 1861Full 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-... | |
| 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 —... | |
| 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... | |
| 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 = */... | |
| 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.... | |
| 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 cannot be exactly... | |
| 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... | |
| William Smyth - Algebra - 1836 - 288 pages
...quantity, plus double the product of the first by the second, plus the second power of the second. double product of the first by the second, plus the...is equal to the difference of their second powers. SECTION V. — ALGEBRAIC FRACTIONS. 55. When the division of two algebraic quantities cannot be exactly... | |
| Robert Mudie - Mathematics - 1836 - 542 pages
...product, and + a 6 — a 6 is =0, and may be left out in adding. Hence we have this principle : — the product of the sum and difference of two quantities is equal to the difference of their squares. If we subtract the square of a — 6 from that of a +6, we have, 4ab — difference. Therefore,... | |
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