 | Ormsby MacKnight Mitchel - Algebra - 1845 - 308 pages
...square of the second. 18. Multiply a+b by a — b. The product is a2 — b2 ; whence we find, that the product of the sum, and difference of -two quantities, is equal to the difference of their squares. These results it is important to retain, as they are of frequent application. Homogeneous... | |
 | Scottish school-book assoc - 1845 - 444 pages
...less than the sum of their squares by twice their product. (See Art. 28, Example 2.) 31. THEOREM III. The product of the sum and difference of two quantities is equal to the difference of their squares. (See Art. 28, Example 3.) NOTE. The above theorems are very important, and should be committed... | |
 | Admiralty - 1845 - 152 pages
...examples afford results which should be firmly fixed in the memory. From the 1st of these we see that " The product of the sum and difference of two quantities, is equal to the difference of the squares of those quantities." From the 2nd of these we see that "The square of the sum of two quantities,... | |
 | Davis Wasgatt Clark - Algebra - 1846 - 374 pages
...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 of two quantities is equal to the difference of their squares. Thus the binomial surd Multiplied by - —Vab+b Gives a +5, a rational quantity. 312. Trinomial... | |
 | Elias Loomis - Algebra - 1846 - 380 pages
...beginners often commit the mistake of putting the square of a — b equal to a2 — b2. THEOREM III. (62.) The product of the sum and difference of two quantities is equal to the difference of their squares. Thus if we multiply a + b By a — b a*+ab — abWe obtain the product a3 — b" EXAMPLES.... | |
 | Charles William Hackley - Algebra - 1846 - 544 pages
...multiply some other given irrational quantity, will produce a rational result ; thus, Again, since the product of the sum and difference of two quantities is equal to the difference of their squares, we have, evidently, =a —b Hence it is obvious that, in these and similar equalities, if... | |
 | Elias Loomis - Algebra - 1846 - 376 pages
...surd 5 + \/ 3 Multiplier 5 — \/ 3 These two examples are comprehended under the Rule in Art. 62, the product of the sum and difference of two quantities is equal to the difference of their squares. Ex. 3. Find a multiplier that shall make \/ 5 + V 3 rational. Ex. 4. Find a multiplier that... | |
 | James Bryce - 1846 - 352 pages
...extended to quadrinomials — See Euc. П., 4, and Exs. 57, 59, Art. 26. Again, from Ex. 5 we see that the product of the sum and difference of two quantities is equal to the difference of their squares ; and conversely, that the difference of the squares of two quantities is equal to the product... | |
 | Horatio Nelson Robinson - Algebra - 1846 - 276 pages
...2a— 3J. Ans. 4a3-— 9J3. Multiply 3y — c by 3y-\-c. Ans. Qy3 — c3. Thus, by inspection we find, the product of the sum and difference of two quantities is equal to the difference of their squares. The propositions included in this article are proved also in geometry. (Art. 14 ) We can sometimes... | |
 | Jeremiah Day - Algebra - 1847 - 358 pages
...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, is equal to the difference of their squares. (Art. 235.) The binomial itself, after the sign which connects the terms is changed from -|-... | |
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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. 
