 | Benjamin Greenleaf - Algebra - 1879 - 350 pages
...Rationalize \/a -\- \/b. Explain the first operation. The second. Repeat the Rule. OPERATION. Since the product of the sum and — difference of two quantities is equal Va + V* to the difference of their squares у*а — y'6 (Theo. III. Art. 78), we multiply the i ,... | |
 | Webster Wells - Algebra - 1880 - 498 pages
...second, plus the square of the second. 106. Again, by multiplication, we have (a + b) (a - b) = a2 - V. (3) That is, The product of the sum and difference...equal to the difference of their squares. EXAMPLES. 107. 1. Square 3 a + 2b. The square of the first term is 9 a2, twice the product of the terms is 12... | |
 | Edward Olney - Algebra - 1880 - 354 pages
...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. The demonstration of these three theorems consists in multiplying x + у by x + y, x — у by x —... | |
 | Popular educator - 1880 - 926 pages
...is, — x — = — aa aaa aaaaa If a -fb be multiplied into a — 6, the product will be a1— Zr ; that is — The product of the sum and difference of two quantities if equal to the difference of their squares. This is an instance of the facility with which general... | |
 | James Mackean - 1881 - 510 pages
...product. III. Multiply a + b by a - b. a + b a - b а2+ ab - ab -V2 a2 -62 Л (a + 6)(а- 6) = a2 -62. That is, the product of the sum and difference of two quantities is equal to the difference of the squares of the quantities. IV. Multiply a2 - o6 + 62 by a + b. a? -ab +62 a +b +63 That is, if... | |
 | William James Milne - Algebra - 1881 - 360 pages
...the quantities ? 2. What sign connects the terms? 79. PRINCIPLE. — The product of the sum and the difference of two quantities is equal to the difference of their squares. 26. (r + *)(r—s). 27. (m -fn) (m — n). 28. (c + a)(c — a). 29. (*-!)(*+!). EXAMPLES. 31. 32.... | |
 | Edward Olney - Algebra - 1882 - 358 pages
...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...equal to the difference of their squares. EXAMPLES. 1. Multiply together 3ax, — Загхг, <íby, — у3, and 2хгуг. 2. Multiply together За;2,... | |
 | Edwin Pliny Seaver, George Augustus Walton - Algebra - 1881 - 304 pages
...Two Quantities. 133. We learn by multiplication that which means that the product of the sum and the difference of two quantities is equal to the difference of their squares. Reversing this formula, we have 134. Exercises. Separate into two factors 78. a 2 -af. 88. 47, 4 -1GPm... | |
 | Popular educator - 1884 - 910 pages
...ie, — x — = aa aaa aaaaa If a + Ъ be multiplied into о — b, the product will bo a*— Tf ; that is — The product of the sum and difference...quantities is equal to the difference of their squares. This is an instance of the facility with which general truths are demonstrated in algebra. If the sum... | |
 | Webster Wells - 1885 - 368 pages
...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...first term is 9 a2, twice the product of the terms is 12a6c, and the square of the second term is 46V. Hence, by formula (1), a+b a +b a2+ab ab +b2 a -b... | |
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... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — b) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares. 
