 ... the square of the second. In the second case, (ab)2 = a?-2ab + bi. (2) That is, the square of the difference of two numbers is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.  A Treatise on Algebra - Page 39by Elias Loomis - 1868 - 384 pagesFull view - About this book
 | Louis Parker Jocelyn - Algebra - 1902 - 460 pages
...+ f2/)2. 10. S2(e+/)+.3(i/ + /t)S2. 165. Theorem 2. The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second. Dem. Let x — a be the difference of two quantities, then... | |
 | Alvord D. Robinson - Arithmetic - 1902 - 572 pages
...ab + ab-b* a2 -b3 From the work, the following principle is derived: — The product of the sum and difference of two numbers is equal to the square of the first minus the square of the second. For the Pupil : 1. State the 3 principles of multiplication. 2. Give the... | |
 | George Edward Atwood - Arithmetic - 1902 - 168 pages
...multiplication to be a2 — 2 a6 + 62. PRINCIPLE. — The square of the difference of two quantities is the square of the first, minus twice the product of the first and second, plus the square of the second. Since a represents any quantity and 6 any less quantity,... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 426 pages
...a' — 2ab + b', which relation may be stated thus : The square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second. In the third case we have (a -f- 6) (a — b) = a' — b», or... | |
 | Edward Gideon - Arithmetic - 1903 - 164 pages
...which is the difference of the two quantities, and the other is the square of the first quantity, plus the product of the first by the second, plus the square of the second quantity. EXAMPLES. 161. a3 + 6'. 171. aV + 1. 181. 8a3 - 6V. 162. ж3 + z2. 172. 1 -6V. 182. a3 +... | |
 | Arthur William Potter - Algebra - 1904 - 182 pages
...compare ? Deduce the following principle : PRINCIPLE. The square of the difference of two quantities is equal to the square of the first minus twice the...first by the second plus the square of the second. Write out the following results without multiplying. If you cannot do this readily, work the examples... | |
 | John William Hopkins - 1904 - 276 pages
...b The required product is the differa2 — ab ence of a(a — 6) and b(a — 6). - ab + ft2 Hence, The square of the difference of two numbers is equal to the square of the first number minus twice the product of the first number and the second number plus the square of the second... | |
 | George Washington Hull - Algebra - 1904 - 172 pages
...(m + n)2. HULL'S EL. OF ALG. — 4 49 PRINCIPLE II. The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second. Thus, by multiplication, а -Ь а —b а2— ab Also,... | |
 | Webster Wells - Algebra - 1904 - 642 pages
...first by the second, plug the square of the second. The square of the difference of two numbers equals the square of the first, minus twice the product of the first bij the second, jilits the square of the second. In the remainder of the book, we shall, for the sake... | |
 | Samuel Jackson - 1904 - 434 pages
...the sum of two numbers is equal to the sum of the squares of the numbers 4- twice the product. (2) The square of the difference of two numbers is equal to the sum of the squares of the numbers — twice the product. (3) The cube of the sum of two numbers is... | |
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