Books Books 1 - 10 of 140 on ... the product of the two, plus the square of the second. In the third case, we.... ... 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. An Introduction to Algebra: Being the First Part of a Course of Mathematics ... - Page 124
by Jeremiah Day - 1827 - 332 pages ## A treatise of algebra: in two books ...

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... ## An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

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... ## An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

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... ## A treatise on navigation, and nautical astronomy

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... ## The Mechanics' Magazine, Museum, Register, Journal, and Gazette, Volume 13

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... ## An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

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 -... ## An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

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... ## An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

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... ## Mathematics for Practical Men

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.... 