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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. "
A Treatise on Algebra - Pągina 189
per Elias Loomis - 1846 - 346 pągines
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A treatise of algebra: in two books ...

William Emerson - 1780 - 531 pągines
...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...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1814 - 303 pągines
...• ' 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...
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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 «- ēos A • ein В, is equal мл — cot2A 1...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1827 - 332 pągines
...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 —...
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The Mechanics' Magazine, Museum, Register, Journal, and Gazette, Volum 13

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

Jeremiah Day - 1832 - 332 pągines
...!/" ' 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...
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Mathematics for Practical Men

Olinthus Gregory - 1833 - 427 pągines
...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....
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Elements of Algebra

William Smyth - 1833 - 280 pągines
...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...
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A treatise on practical geometry, mensuration, conic sections, gauging, and ...

Ireland commissioners of nat. educ - 1834
...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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Mathematics for Practical Men: Being a Common-place Book of Principles ...

Olinthus Gregory - 1834 - 427 pągines
...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...
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