 | 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... | |
| |
The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second. 
