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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. "
An Introduction to Algebra: Being the First Part of a Course of Mathematics ... - Página 124
por Jeremiah Day - 1827 - 332 páginas
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1814 - 303 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...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1820 - 332 páginas
...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...
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A treatise on navigation, and nautical astronomy

Edward Riddle - 1824 - 551 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...
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The Mechanics' Magazine, Museum, Register, Journal, and Gazette, Volumen13

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 - 1831 - 332 páginas
...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 -...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1832 - 332 páginas
...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...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1832 - 332 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...
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Elements of Algebra

William Smyth - 1833 - 280 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...
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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 páginas
...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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