| Wisconsin - Wisconsin - 1879 - 1240 pages
...sides are together equivalent to the squares of the diagonals. 2. Demonstrate, geometrically, that the product of the sum and difference of two quantities is equal to the difference of their squares, 3. Prove that, if from the same point without a circle a tangent and a secant be drawn, the tangent... | |
| 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... | |
| 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... | |
| 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 ,... | |
| Edward Olney - Algebra - 1880 - 354 pages
...to the 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...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
...to the 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...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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