 ... 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 - Pàgina 189per Elias Loomis - 1846 - 346 pàginesVisualització completa - Sobre aquest llibre
 | Silas Totten - 1836 - 360 pàgines
...place of a and b, it follows, that this property is general. This property may be thus enunciated : — The product of the sum and difference of two quantities is equal to the difference of their squares. Having demonstrated this property, we can make use of il to shorten the operation of multiplication... | |
 | 1836 - 488 pàgines
...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... | |
 | 1837 - 136 pàgines
...of this rule is evident from 47. I. and from a Cor. to 5. II. which says, that the rectangle under the sum and difference of two quantities is equal to the difference of their squares. (Page 33.) 17. By the 8. VI. AB X BD = BC2. Hence, BD B С2 = -T~D, which is one part of the rule.... | |
 | James Bryce - 1837 - 322 pàgines
...of the form itya will be made rational, by the multiplier 6^/o"-1; for 4/0 X ^/a""'=:^/an=o. Also, since the product of the sum and difference of two quantities is the difference of their squares (Ex. 5, 12, Art. 38), it follows that \/а±\/b will be made rational... | |
 | Charles Frederick Partington - 1838 - 1116 pàgines
...minus twice the product of the first and second. 3°. That (a + i) (a — i) = a3 — i3 ; or, that the product of the sum and difference of two quantities is equal to the difference of their squares. These examples are of very frequent occurrence in algebra, and their results should be well remembered,... | |
 | Andrew Bell (writer on mathematics.) - 1839 - 500 pàgines
...example ; and therefore а + x is the sum, and а—x the difference of a and x, hence; — (70.) 1 The product of the sum and difference of two quantities is equal to the difference of their squares.1 * EXERCISES. 1. Multiply 2a2 — 4 ая: + 2 ж2 by За — Zx 2. Multiply 3 a4 + 3ж4 by... | |
 | Thomas Sherwin - 1841 - 314 pàgines
...gives a \/(a " r/P" . //(a + z)4 1//^(rt-lz)4 a* a^ z^ - - -j- - = - - -j- - ; also, — = , ._t = ~ ~ x Since the product of the sum and difference of two quantities is the difference of their second powers, Art. 33, if we would 1/2^ render the denominator of — - —... | |
 | Thomas Sherwin - 1841 - 320 pàgines
...\/ax z V/6" In like manner, multiplying both terms of the fraction _ 3 bj / 6 . 6 a + za + x x- x'x z Since the product of the sum and difference of two quantities is the difference of their second powers, Art. 33, if we would V/2 render the denominator of — ;. -... | |
 | Wales Christopher Hotson - 1842 - 306 pàgines
...Required the square of a + b. a -\-b a +b a?+ ab (4) Multiply a + b by a — b. Hence it appears, that the product of the sum and difference of two quantities is equal to the difference of their squares, which is proved in Prop. 5, Book n. of Euclid's Elements, and furnishes a most useful rule for the... | |
 | James Bates Thomson - 1844 - 272 pàgines
...y"y3. 20. If a-\-b be multiplied into a — b, the product will be a2— 62, (Art. 86 ;) that is, 19 1. The product of the sum and difference of two quantities, is equal to the difference of their squares. This is an instance of the facility with which general truths are demonstrated in algebra. If the sum... | |
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