 | Webster Wells - Algebra - 1879 - 468 pages
...first by the second, plus the square of the second. 106. Again, by multiplication, we have That is, The product of the sum and difference of two quantities is equal to the difference of their squares. EXAMPLES. 107. 1. Square 3 a + 2 b. The square of the first term is 9 a2, twice the product of the... | |
 | Thomas K. Brown - Algebra - 1879 - 292 pages
...difference of the squares of the two quantities. This may be more briefly expressed thus : Theorem III. — The product of the sum and difference of two quantities is equal to the difference of their squares. SECTION XXVIII. USE OF THEOREMS IN MULTIPLICATION. 77. Ex. What is the square of x + y ? SOLUTION,... | |
 | Benjamin Greenleaf - Algebra - 1879 - 350 pages
...containing only the square root. 1. Rationalize \/a -f- \/b. OPERATION. Since the product of the earn and — , difference of two quantities is equal • '- to the difference of their squares y/g — y/6 (Theo. III. Art. 78), we multiply the i j—l given binomial by the same terms. with one... | |
 | 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 ,... | |
 | Shelton Palmer Sanford - Algebra - 1879 - 348 pages
...Ans. - . 20. Square (a" - 1). Ans. a»n - 2a" + 1. THEOREM III. 69. The product of the SUM and the DIFFERENCE of two quantities is equal to the difference of their squares. Ex. 1. What is the product of (a +6) multiplied by (a- 6)? OPERATION. a + 6 Analysis. Multiplying (a... | |
 | 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 —... | |
 | James Mackean - 1881 - 510 pages
...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 is equal to the difference of their squares. EXAMPLES. 1. Multiply together 3ax, — Загхг, <íby, — у3, and 2хгуг. 2. Multiply together... | |
 | 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... | |
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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. 
