 | Richard Dawes - Teaching - 1849 - 228 pages
...formulae is of service. For instance, that (1.) (a + li) (a — b}=.a- — i': that this means that the sum of two quantities multiplied by their difference is equal to the difference of their squares. (2.) That (a + J)' = a5 + 2a J + *', or that the square of the sum of two thoroughly to understand,... | |
 | Daniel Adams - Arithmetic - 1849 - 142 pages
...subtracting the area of the less circle from the area of the greater. The product of the sum of the diameters multiplied by their difference, is equal to the difference of their squares. (See IT 42.) EXAMPLES FOR PRACTICE. 1. Within a circular park 15 rods in diameter, is a circular pond... | |
 | Charles Davies - Algebra - 1850 - 292 pages
...square of 7a2b2 — I2ab3. We have 4O. Let it be required to multiply a+b by a— b. We have Hence, the sum of two quantities, multiplied by their difference, is equal to the difference of their square* : 1. Multiply 2c-\-b by 2c—b. We have 2. Multiply 9ac+3bc by Sac— 3bc. We have (9ac+3bc)(9ac—... | |
 | Daniel Adams - Measurement - 1850 - 144 pages
...subtracting the area of the less circle from the area of the greater. The product of the sum of the diameters multiplied by their difference, is equal to the difference of their squares. (See 1T 42.) EXAMPLES FOR. PRACTICE, 1. "Within a circular park 15 rods in diameter, is a circular... | |
 | Horace Mann - 1851 - 384 pages
...2016; 44X46 = 2024 ; 7 X 8 = 56, and 72 X 78 = 5616 ; 71 X 79 = 5609, &c. (12.) The sum of two numbers multiplied by their difference, is equal to the difference of their squares. Hence we may readily find the product of two numbers, one of which is as much above as the other is... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...loth terms by such a factor as will render the exponent of the given radical equal to unity. Since the sum of two quantities, multiplied by their difference, is equal to the difference of their squares (Art. 80) ; if the fraction is of the form , and we multiply both terms by i — Jc, the denominator... | |
 | Joseph Ray - Algebra - 1848 - 250 pages
...form —=,, if we multiply both terms Vb by i/6, the denominator will become rational. Thus, Since the sum of two quantities, multiplied by their difference, is equal to the difference of their squares ; if the fraction is of the form -_, and we multiply both terms by 6— i/c, the denomin6+i/c ator... | |
 | Ezra S. Winslow - Business mathematics - 1853 - 264 pages
...triangles, ADC and BDC, DC a leg common to both. Or, A/(AC-f AD X AC— AD) = DC ; for the sum of any two quantities multiplied by their difference is equal to the difference of their squares. -£2 + i BC = B g, and V(ABS - B?) = A g, perpendicular to BC produced. ^ - * °2 + y = A h, and V(AB2... | |
 | John Radford Young - 1855 - 218 pages
...multiplied by — 4a'6x3. In like manner, the second factor in (7) is 7a'*-4. 3. The sum of two numbers multiplied by their difference is equal to the difference of their squares. Thus, take the two numbers 7 and 3 ; their sum is 10, and 102=72 + 32 + 21 x 2 = 100. The difference... | |
 | Charles W. Hackley - Engineering - 1856 - 530 pages
...n, and CG = R x tangent $ m ; Ave have therefore DG tangent = 800 ft., n — 16 6 and m — 12°. * The sum of two quantities multiplied by their difference is equal to the difference of their squares. ___ __ „_ ___ ^^ 398 Iff800 __ '800 __ .. £ m ~~ tan. 8°'+ tan. 6C'~ •HoEI+^l'oslO ~ 32oG'' 3256-7... | |
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The sum of two numbers multiplied by their difference, is equal to the difference of their squares. 
