 ... 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 - Página 204por Elias Loomis - 1868 - 384 páginasVista completa - Acerca de este libro
 | William Emerson - 1780 - 574 páginas
...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 páginas
...• ' 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 páginas
....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 páginas
...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 páginas
...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 páginas
...multiplied 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, is equal to the difference of their squares. (Art. 235.) The binomial itself, after the sign which connects the terms is changed from -\-to-, or... | |
 | Jeremiah Day - 1832 - 354 páginas
...!/" ' 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 páginas
...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... | |
 | Olinthus Gregory - 1834 - 472 páginas
...changing its value ; while the expression becomes freed from the surds in the denominator, because the product of the sum and difference of two quantities is equal to the difference of their squares. Examples. 8 v/5+ y/3 _ 8 (у'б + y/3) — v/3 ' v/5 + v/3 ~ ~ 8~ _ __ v/5 + ^2 v/5 + v/2 'v/5— v/2... | |
 | Ireland commissioners of nat. educ - 1834 - 370 páginas
...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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