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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. "
Elements of Algebra: Including Sturm's Theorem - Page 33
1847 - 368 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 - 378 pages
...That is, the square of the difference between two quantities is composed of the square of the first, minus twice the product of the 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
...in another manner : via;. The square of any polynomial contains the square of ihe first term, plus twice the product of the first by the second, plus the square of the second ; plus twice the product of the first two terms by the third, plus the square of the third ; plus twice...
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First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - Algebra - 1839 - 272 pages
...have That is, the square of the difference between 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. 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

Algebra - 1839 - 368 pages
...(a—b)=az—2ab+b3: That is, the square of the difference between 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. Thus, (7o3i3— 12ai3)3=49o4i4— 168a3i5+144a3i6. 3d. Let it be required to multiply a-\-b by a —...
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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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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1842 - 284 pages
...(a—b)—az~2ab+bz. That is, the square of the difference between 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, 1. Form the square of 2a— b. We have (2a—6)2=4o2—4a6+62. 2. Form the square of 4ac—bc. We have...
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Elements of Algebra

Charles Davies - Algebra - 1842 - 368 pages
...—2ai+i2: That is, the square of the difference between 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. Thus, (7o 2 i2—12ai 3 ) 2 =49a 4 i 4 —168a 3 i 6 +144a 2 i 6 . 3d. Let it be required to multiply...
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An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - Algebra - 1845 - 308 pages
...perceive, that 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. 18. Multiply a+b by a — b. The product is a2 — b2 ; whence we find, that the product of the sum,...
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