 | 1837 - 136 σελίδες
...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.... | |
 | Charles Frederick Partington - 1838 - 1116 σελίδες
...second, 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,... | |
 | John Radford Young - 1838 - 368 σελίδες
...difference of two cube roots. In the former case the multiplier will be suggested from the property, that the product of the sum and difference of two quantities is the difference of their squares. In the latter case the multiplier will be a trinomial surd, consisting... | |
 | Andrew Bell (writer on mathematics.) - 1839 - 500 σελίδες
...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... | |
 | John Radford Young - 1839 - 332 σελίδες
...difference of two cube roots. In the former case the multiplier will be suggested from the property, that the product of the sum and difference of two quantities is the difference of their squares. In the latter case the multiplier will be a trinomial surd, consisting... | |
 | Jeremiah Day - 1841 - 354 σελίδες
...x Va = a- And \/ax Va"= Va'= a. And Vax (/(fa, &c. And (a+6)* x(a+6)'=a+6. And (x+yrx(x+y)*=*+y. 3. c. A factor which will produce a rational product,...the sign which connects the terms is changed from -f- to— , or fiom-to-f-, will be the factor required. Thus (Va+y&) x (Va - V6) = Va3 ~ A/63= a -... | |
 | Wales Christopher Hotson - 1842 - 306 σελίδες
...(3) 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... | |
 | Davis Wasgatt Clark - 1844 - 394 σελίδες
...this form, v/0+v/6, or a+^/b, are called binomial surds, and may be reduced to rational quantities on the principle that the product of the sum and difference...quantities is equal to the difference of their squares. Thus the binomial surd v/a+v/6 Multiplied by - . v/o — -J/b — Vab+b Gives - - . a +b, n. rational... | |
 | James Bates Thomson - 1844 - 272 σελίδες
...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... | |
 | Horatio Nelson Robinson - 1844 - 184 σελίδες
...parts. Also, that («-|-i)(a — i)=a2 — b-. Or (a4+i4)O4— J4)=a2— b2. That is, the rectangle of the sum and difference of two quantities is equal to the difference of their squares. By this last observation we readily perceive that a4— b4, or any other binomial having a minus sign... | |
| |
... 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. 
