| William Smyth - Algebra - 1830 - 264 pages
...power or square of the sum of two quantities contains the square of the first quantity, plus double **the product of the first by the second, plus the square of the second.** Thus, (7 + 3) (7 + 3) or, (7 + 3)' = 49 + 42 + 9 = 100 So also (5 a2 + 8 a2 6)2 = 25 a6 + 80 <tb +... | |
| Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 389 pages
...enunciated in another manner : viz. The square of any polynomial contains the square of the first term, plus **twice the product of the first by the second, plus the square of the second;** plus twice the product of each of the two first terms by the third, plus the square of the third; plus... | |
| Charles Davies - Algebra - 1835 - 374 pages
...(a-by=(ab) (ab)=a1-2ab+V That is, the square of the difference between two quantities is composed of **the square of the first, minus twice the product of...first by the second, plus the square of the second.** Thus, (7a3i3-12ai3)3=49aW-168a''is+144a3ii1. 3d. Let it be required to multiply a+b by a— b. We have... | |
| Algebra - 1838 - 372 pages
...difference, a — b, we have (a-by=(ab) (ab)=a?-2ab+t2 : That is, the square of the difference between **two quantities is equal to the square of the first, minus twice the product of the** frst by the second, plus the square of the second. Thus, fTVi2— 12ai3)2=49a4i4— 168a3i5+144a2i6.... | |
| Charles Frederick Partington - Encyclopedias and dictionaries - 1838 - 1116 pages
...the product of the first and second. 2°. That (o — b) (a — i) = a* — 2o6 + V ; or, that the **square of the difference of two quantities is equal to the square of the first,** plug the square of the second, minus twice the product of the first and second. 3°. That (a + i) (a... | |
| Charles Davies - Algebra - 1839 - 272 pages
...39. To form the square of a difference a— b, we have That is, the square of the difference between **two quantities is equal to the square of the first,...first by the second, plus the square of the second.** 1 Form the square of 2a — b. We have 2. Form the square of 4ac — be. We have (4 ac — be)2 —... | |
| Bourdon (M., Louis Pierre Marie) - Algebra - 1839 - 324 pages
...difference, a — b, we have (a— 6)2=(a-6) (a-6)=a2-2a6 + 62: That is, the square of the difference between **two quantities is equal to the square of the first,...first by the second, plus the square of the second.** Thus, (7a262— 12a63)2=49a4M— 168a365+144a266. 3d. Let it be required to multiply a+6 by a — b.... | |
| Charles Davies - Algebra - 1839 - 252 pages
...principles, That is, the square of the sum of two quantities is equal to the square of the first, plus **twice the product of the first by the second, plus the square of the second.** 1. Form the square of 2a+36. We have from the rule (2a + 36)2 = 4<z3 + 12ab + 962. 2. (5a6 + 3<zc)2... | |
| Charles Davies - Algebra - 1840 - 264 pages
...39. To form the square of a difference a— b, we have That is, the square of the difference between **two quantities is equal to the square of the first, minus twice the product of** tht frst by the second, plus the square of the second. 1 Form the square of 2<z— b. We have (2a —... | |
| Charles Davies - Algebra - 1841 - 264 pages
...J)=a2— 2aJ+J2. That is, the square of the difference between two quantities is equal to the squajre **of the first, minus twice the product of the first by the second, plus the square of the second.** 1 Form the square of 2a— b. We have (2a — J)2=4a2 — 4aJ+J2. 2. Form the square of 4ae — be.... | |
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