| James Bates Thomson - Algebra - 1878 - 324 pages
...a-' + 2ab + V. a + rtO Hence, the + ab + b3 FORMULA, (a+b)9 = <P+2db-\-&. Ans. a' + tab + b9 102. The **square of the difference of two quantities is equal to the square of the first, minus twice** their product, plus the square of the second. 2. Let it be required to multiply a — b by a — b.... | |
| Edward Olney - Algebra - 1878 - 516 pages
...+ 3a3£s. jfesutt, 25a - 4 + 30o6» + 9a<*«. 5. Square ^16 - * + fa? -' 6 - '. 95. THEO. — Tlve **square of the difference of two quantities is equal to the square of** tlie first, minus twice the product of the first by tlie second, plus the square of the second. DEM.... | |
| Shelton Palmer Sanford - Algebra - 1879 - 348 pages
...point, and, multiply ing a2+2a6 + 62 by (a -H6), he will have the expansion required* THEOKEM H. 68. The **square of the DIFFERENCE of two quantities is equal...first by the second, plus the square of the second.** Ex. 1. Find the square of (a — 6). Analysis. Here a and 6 are the two quantities, and OPERATION (a... | |
| Webster Wells - Algebra - 1879 - 468 pages
...second. 105. "We may also show, by multiplication, that (a — 6)2 = a2 — 2 ab + b2. (2) That is, The **square of the difference of two quantities is equal to the square of the first, minus twice** thg product of the first by the second, plus the square of the second. 106. Again, by multiplication,... | |
| Benjamin Greenleaf - 1879 - 348 pages
...sum and difference of two >'quanti- . f • ties is equal to the difference of their squares. .stet'f **For, let a represent one of the quantities, and b the other** ; -• '^^u, then, (a + 6) X(<>-6)-4> — P. which agrees with the theorem. EXAMPLES. 1. Find the product... | |
| Thomas K. Brown - Algebra - 1879 - 292 pages
...in which we cannot tell at once what the root is. Theorems I. and II. are, The square of the gum or **difference of two quantities is equal to the square of the first,** =t twice the product of the first and second, + the square of the second. Therefore we first take the... | |
| Webster Wells - Algebra - 1880 - 512 pages
...the second. 105. We may also show, by multiplication, that (a - b)2 = a2-2ab + b2. (2) That is, The **square of the difference of two quantities is equal...first by the 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... | |
| Charles Scott Venable - Algebra - 1880 - 168 pages
...Zab + V. . . . (B), which expresses the Rule :—Tlie square of the difference of two quantities is **the square of the first, minus twice the product of...first by the second, plus the square of the second.** Ex. 1. (x - 5)" = x' - 10ж + 25. Ex. 2. (За - 2o)" = (За)' - 2 x За х 2o + (2o)' = 9a' - 12ao... | |
| Edward Olney - Algebra - 1880 - 354 pages
...square of the first, plus twice the product of the two, plus the square of the second. 86. THEO. — The **square of the difference of two quantities is equal...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... | |
| Joseph Ray - Arithmetic - 1880 - 420 pages
...principle : PRINCIPLE. — The square of the sum of two numbers is equal to the square of the first, plus **twice the product of the first by the second, plus the square of the second.** Thus : Show by involution, that : \. (5)2 equals 25. 8. (£)5 equals MrlJ. 2. 14s 2744. 9. (.02) s... | |
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