Books Books 1 - 10 of 142 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 - 1842 - 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... ## 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... ## An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1827 - 332 pages
...y~3Xy*=y° = l. 235. If 0+6 be multiplied into 0 — 6, the product will be n3-6* : (Art. 110,) that is TlIE PRODUCT OF THE SUM AND DIFFERENCE OF TWO QUANTITIES, IS EQUAL TO THE DIFFERENCE OF THEIR SQUARES. T'lis is another instance of the facility with which general truths are demonstrated in algebra. See... ## 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... ## Mathematics for Practical Men

Olinthus Gregory - 1833 - 427 pages
...quantities 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.... ## Elements of Algebra

William Smyth - Algebra - 1833 - 280 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... ## Mathematics for Practical Men: Being a Common-place Book of Principles ...

Olinthus Gregory - Mathematics - 1834 - 427 pages
...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... ## A treatise on practical geometry, mensuration, conic sections, gauging, and ...

...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... ## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...multiplication between them. Powers of the same root may be multiplied, by adding their expoDents. The product of the sum and difference of two quantities is equal to the difference of their squares. Powers may be divided, by rejecting from the dividend, a factor equal to the divisor ; or by placing... 