 | Jeremiah Day - 1859 - 422 σελίδες
...And 'x+y)"X(x+y) * —x+y. And V«XV«3=«, &c. And (a+b)^X(a+b)%=a+b. And (x+y)fX(x+y)%=x+y. 3O7. A factor which will produce a rational product, when...is equal to the difference of their squares. (Art. 111.) The binomial itself, after the sign which connects the terms is changed from + to — , or from... | |
 | John Fair Stoddard, William Downs Henkle - 1859 - 538 σελίδες
...11, Square 2z-<"-1)yJ^J'-5«*L-1y I • w+nt-3 ..."M-"12, Square^ = y r— 4« THEOREM III. (111.) The product of the sum and difference of two quantities is equal to the difference of their squares. DEMONSTRATION. Let a + b and a—b represent respectively the sum and difference of two quantities.... | |
 | James B. Dodd - 1859 - 368 σελίδες
...with a sign changed. Thus (/3+v/2)x(/3— /2)=3 — 2=1. The product in this case is readily found on the principle, that the Product of the sum and difference of two quantities is equal to the dif ference of the squares of the two quantities. 3. A trinomial containing irrational square roots... | |
 | Silas Lawrence Loomis - 1859 - 324 σελίδες
...1849. Or by Prin. 2 : 43 = 40 + 3. 432 = 1600 + 2x 120 + 9 = 1849. 358. PRIN. 4. — THE PRODUCT or THE SUM AND DIFFERENCE OF TWO QUANTITIES, IS EQUAL TO THE DIFFERENCE OF THEIR SQUARES. ILLUSTRATION. — 11+ 7 = 10. 11— 7 = _4 121 — 49 = 72. Ans. 3«59. PRIN. 5. — EVERY NUMBER MAY... | |
 | Charles Hutton - 1860 - 1020 σελίδες
...To find multipliers which will render binomial surds rational. produce a rational result; and since the product of the sum and difference of two quantities is equal to the difference of their squares, we have, evidently, 'a = a; (-v/a — л/*) (Va+Vb) = a — b x1 = *; (x + Vy) (* - Vy] = *4-y y-^y!... | |
 | Horatio Nelson Robinson - 1863 - 432 σελίδες
...the first and second, plus the square of the second. III. (ti+6) (a— Z»)=a'— b3 Or, in words, The product of the sum and difference of two quantities is equal to the difference of their squares. By the aid of these formulas we are enabled to write the square of any binomial, or the product of... | |
 | Gerardus Beekman Docharty - 1862 - 336 σελίδες
...(f-î)'= If we multiply af 6 by a— ¿), we shall have From which we derive the following THEOREM III. The product of the sum and difference of two quantities is equal to the difference of the squares of those quantities. EXAMPLES. 1. (3xm+2y")(3xm-2if)=9x*"-4y'". Ans. 2. (ж+|)(ж-1)= Ans.... | |
 | Benjamin Greenleaf - 1863 - 338 σελίδες
...62 — 10 a2 W ? Ans. 25 а4 64 — 100 a4 6s + 100 a4 6e. THEOREM III. Î8. The product of the sinn and difference of two quantities is equal to the difference of their squares. For, let a represent one of the quantities, and b the other ; then, (a + 6) X (a — 6) = a' — V,... | |
 | Olinthus Gregory - 1863 - 482 σελίδες
...the expression becomes freed from the surds in the denominator, because the product of the sum oiid difference of two quantities is equal to the difference of their squares. Examples. r-: 8 = 8 v/5 + v/3 — 8 (v/5 + v/3) _ - v/5 — v/3 v/5 — v/3 -y/5 + v/3 ~ 3 4 (v/5 +... | |
 | Horatio Nelson Robinson - 1864 - 444 σελίδες
...product of the first and second, plus the square of the second. III. O+&) (a— i)=a'— V Or, in words, The product of the sum and difference of two quantities is equal to the difference of their squares. By the aid of these formulas we are enabled to write the square of any binomial, or the product of... | |
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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. 
