 | 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*, —... | |
 | 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,... | |
 | 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) =... | |
 | 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... | |
 | 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... | |
 | 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 —... | |
 | James Bates Thomson - 1878 - 322 páginas
...Radical Binomial to a Rational Quantity. i. It is required to rationalize \/« + Vb. ANALYSIS. — The product of the sum and difference of two quantities is equal to the difference of their squares (Art. 103) ; therefore, (y'aH <\/&) multiplied by ( y^-y's) = a— 6, which is a rational quantity.... | |
 | Edward Olney - 1878 - 360 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 Ъах, — 3a*xs, kby, — y3, and 2z*y9. • 2, Multiply together... | |
 | Benjamin Greenleaf - 1878 - 338 páginas
...the square of 5 a2 i2 — 10 a2 V ? Ans. 25 a4 64 — 100 a4 b% + 100 a4 66. THEOREM III. 78i TJ1e product of the sum and difference of two quantities is equal to the difference of their squares. For, let a represent one of the quantities, and 6 the other ; then, (a + 6) X (« — 6) = «' —... | |
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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. 
