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" 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. "
New Elementary Algebra: Designed for the Use of High Schools and Academies - Page 54
by Benjamin Greenleaf - 1879 - 309 pages
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Elements of Algebra

William Smyth - Algebra - 1830 - 278 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 +...
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Elements of Algebra: Tr. from the French of M. Bourdon, for the ..., Volume 1

Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 446 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...
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Elements of Algebra: Tr. from the French of M. Bourdon. Revised and Adapted ...

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...
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Elements of Algebra

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....
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The British Cyclopaedia of the Arts, Sciences, History, Geography ...

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...
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First Lessons in Algebra: Embracing the Elements of the Science

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 —...
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Elements of Algebra

Bourdon (M., Louis Pierre Marie) - Algebra - 1839 - 368 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....
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First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - Algebra - 1839 - 264 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...
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First Lessons in Algebra: Embracing the Elements of the Science

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 —...
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First Lessons in Algebra: Embracing the Elements of the Science

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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