 | Robert Wallace - 1870 - 164 páginas
...theorem for finding the product of the sum and difference of two quantities is deduced. THEOREM III. — The product of the sum and difference of two quantities is equal to the difference of the squares of those quantities. EXAMPLES. 3xm -\-2y°) (3xm — 2y")=9a;2m — 4^-°. Ans. a;+*)(a;-$)=a;2—... | |
 | James Haddon - 1871 - 244 páginas
...difference of two quantities is equal to ' the sum of their squares, diminished by twice their product. 3. The product of the sum and difference of two quantities is equal to the difference of their squares. The student is recommended to commit these three theorems to memory. DIVISION. VII Division is just... | |
 | William Frothingham Bradbury - 1872 - 262 páginas
...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—... | |
 | Daniel Barnard Hagar - 1873 - 278 páginas
...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 páginas
...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 páginas
...(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 páginas
...-|- 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 páginas
...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... | |
 | Edward Olney - 1877 - 466 páginas
...— 12а"Ь~" + 96~7. 4. Square m ~p — n~q. Result, т-" — 2т~гп-' + п~*. lm 96. THEO. — The product of the sum and difference of two quantities is equal to the difference of their squares. DEM. — Let x and y be any two quantities. Their sum is x -\- y, and their difference is x — y.... | |
 | William Frothingham Bradbury - 1877 - 280 páginas
...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 —... | |
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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. 
