 | William Frothingham Bradbury - 1872 - 262 σελίδες
...28) B D2 = A B2 — A D2 B _ 46V— (6»+ c2 — a*)' _ AC X BD _ 6 ! iV ;*—(i? + a' — 6')' 16 As the product of the sum and difference of two quantities is equal to the difference of their squares, we have But 2 be — (62 + c' — a2) = a2 — (I2— 2 be -\- c2) = a2— (6 — c)a and a2— (6—... | |
 | Elias Loomis - 1873 - 396 σελίδες
...of the equation taken with the contrary sign. If we multiply together the two values of x (observing that the product of the sum and difference of two...quantities is equal to the difference of their squares), we obtain . . JD2 / pz\ £-(«+?)=-* Thus, in the equation a;2— Wx=— 16, the product of the two... | |
 | Daniel Barnard Hagar - 1873 - 278 σελίδες
...a*-2a? + 1. 4. What is the square of 3a*-8a2? 5. Expand (5s3 - 2cd)(5a;s - 2cd). Ttieorem III. 115. The product of the sum and difference of two quantities is equal to the difference of their squares. For, let a and b represent the two quantities, then a+b will denote their sum, and a — b their difference,... | |
 | Edward Olney - 1873 - 354 σελίδες
...square of the first, minus twice the product of the two, plus the square of the second. 87. THEO. — The product of the sum and difference of two quantities is equal to the difference of their squares. EXAMPLES. 1. Multiply together 3ax, — 3a*x*, 4by, — y*, and %x*y*. 2. Multiply together 3x*, —... | |
 | Charles Mansford - 1875 - 110 σελίδες
...(2œ-36)2 = (2a)2 - 2.2ax36 + (36)" = 4a2 - 12a6 + 96" Examples I to 12 in Ex. xviii. Prom iii. we see that The product of the sum and difference of two...quantities is equal to the difference of their squares. JUVISION. = 9.г~ — Examples 13 to 18 in Ex. xviii. Now look at the ivth. result. (x+а)(x+Ъ) =... | |
 | William Frothingham Bradbury - 1875 - 280 σελίδες
...-|- y2. 2. 2 ж — 4 у. 3. ж— 1. Ans. x2 — 2ж + 1. 4. 7ж-2. <# THEOREM IV. ^ ¿A 60i ÎTie product of the sum and difference of two quantities is equal to the difference of their squares. Let a -|- 6 be the sum, and a — 6 the difference of the two quantities a and h. PROOF. a + 6 a —b... | |
 | Horatio Nelson Robinson - 1875 - 430 σελίδες
...product of the first and second, plus the square of the second. III. (a +b)(a — b)—a*-^; hence, Tue 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... | |
 | William Frothingham Bradbury - 1877 - 280 σελίδες
...y1. 2. 2 x — 4 у. 3. a;— 1. Ans. x2 — 2x + 1. 4. 7x — 2. THEOREM IV. 60. Tlw product of tlie sum and difference of two quantities is equal to the difference of their squares. Let a -j- b be the sum, and a — b the difference of the two quantities a and It. PROOF. a + 6 a —... | |
 | Edward Olney - 1877 - 466 σελίδες
...sum and difference of their square roots. DEM. — This is an immediate consequence of the theorem, that "The product of the sum and difference of two quantities is the difference of their squares. " Thus o2 — 6s = (a + 6) (o — 6). Also, if we have m — n, m... | |
 | James Bates Thomson - 1878 - 322 σελίδες
...traveling being 13 hours. How far did he walk? j I % 26. Given b -- ^— = o, to find x. i — x 27. Prove that the product of the sum and difference of two...quantities, is equal to the difference of their squares. 28. Prove that the product of the sum of two quantities into a third quantity, is equal to the sum... | |
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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. 
