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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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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1842 - 258 pages
...a— b, we have (a—b)2 = (a—b) (a—b)—az~2ab+bz. 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 (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
...difference, a—b, we have (a—b)2=(ab) (ai)=a 2 —2ai+i2: 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, (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 - 294 pages
...second. 17. Multiply a — b by a — b. The product is a2 — 2a6+62 ; from which we perceive, that the square of the difference of two quantities, is equal...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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Elements of Algebra: Including Sturms' Theorem

Charles Davies - Algebra - 1845 - 368 pages
...36a862 + 108a5ft* + 81a2ft6 ; also, (8a3 + 7acb)2-. THEOREM II. 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 tecond, plus the square of the second. Let a represent one of the quantities and b the other : then...
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 380 pages
...common mistakes of beginners is to call the square of а + b equal to a2 + 62. THEOREM II. (61.) The square of the difference of two quantities, is equal...of the first, minus twice the product of the first and second, plus the square of the second. Thus if we multiply a — b By a — b We obtain the product...
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 346 pages
...common mistakes of beginners is to call the square of o + b equal to a2 + 62. THEOREM II. (61.) The square of the. difference of two quantities, is equal...of the first, minus twice the product of the first and second, plus the square of the second. Thus if we multiply a — b By a — b a2—ab — ab We...
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Elements of Algebra: Including Strums' Theorem

Algebra - 1847 - 368 pages
...36a╗62 + 108a56* + 8 la2*6 ; also, (8a3 + 7ac6)2=. THEOREM II. 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. Let a represent one of the quantities and b the other : then a — b = their difference. Now, we have...
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Elements of Algebra: Including Sturm's Theorem

Algebra - 1847 - 368 pages
...THEOREM II. The square of the difference between two quantities is equal to the square of the ▀rst, minus twice the product of the first by the second, plus the square of the second. Let a represent one of the quantities and b the other : then a — b = their difference. Now, we have...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 250 pages
...a— b a2 — ab —a6+6' But a—b is the difference of the quantities a and 6; hence THEOREM II. The square of the difference of two quantities, is equal...first by the second, plus the square of the second. EXAMPLES. 1 (5— 4)2=25— 40+16=1. 2. (2a— 6)2=4a2-4a6+62. 3. (3x- 22/)2=9x2-12xy+4y2. 4. (^-y2)s=x4-2xy+/....
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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1848 - 300 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<z — i)2 = 4a2 — 2. Form the square of 4<zc— be. We...
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