 | Wisconsin. Department of Public Instruction - 1879 - 380 páginas
...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 - 1879 - 292 páginas
...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,... | |
 | Wisconsin - 1879 - 1240 páginas
...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... | |
 | Webster Wells - 1879 - 468 páginas
...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... | |
 | Benjamin Greenleaf - 1879 - 350 páginas
...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 - 1879 - 350 páginas
...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 - 1879 - 348 páginas
...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 - 1880 - 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. The demonstration of these three theorems consists in multiplying x + у by x + y, x — у by x —... | |
 | James Mackean - 1881 - 510 páginas
...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 - 1881 - 360 páginas
...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.... | |
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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. 
