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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 and second, plus the square of the second. "
The first principles of algebra, for the use of the boys of the Royal ... - Page 23
by Admiralty - 1845
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First Lessons in Algebra: Being an Easy Introduction to that Science ...

Ebenezer Bailey - Algebra - 1835 - 258 pages
...a — b 1 fe — 6 a — b a2 — 06 . . ' _ a 6 4. 62 n *- 2 ab + 6s. That is, <Ae second power of the difference of two quantities is equal to the sum of their second powers, diminished by twice their product. . , 20. An artist sold to A and B two pictures for...
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A New Introduction to the Science of Algebra...

Silas Totten - Algebra - 1836 - 360 pages
...adding them together : thus, and 36aV + 60a3^3 + 25aix3 = (Sax2 + 5aV)2, or x X (6ax2 + 5aV). . 2. The square of the difference of two quantities is...the sum of their squares, minus twice their product. Let a be the greater of two quantities, and b the lesSi then a — b will be the difference and (a...
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A New Introduction to the Science of Algebra ...

Silas Totten - Algebra - 1836 - 332 pages
...thus, X (8a25 + 10a6), and 36a2^ + 60a3#3 + 25a4#2 = (6a#2 + 5a2#)2, or 2-) x (6a#2 + 5as#). 2. 7Vte square of the difference of two quantities is equal...the sum of their squares, minus twice their product. Let a be the greater of two quantities, and b the less, then a — b will be the difference, and (q...
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The British Cyclopaedia of the Arts, Sciences, History, Geography ...

Charles Frederick Partington - Encyclopedias and dictionaries - 1838 - 1116 pages
...plus twice 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....
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An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - Algebra - 1845 - 308 pages
...the 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 to the square of the first minus twice the product of the first by the second, plus the square of the second....
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 380 pages
...most 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 to the square of the first, minus twice the product of the first and second, plus the square of the second....
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 376 pages
...most 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 to the square of the first, minus twice the product of the first and second, plus the square of the second....
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A Treatise on Algebra: For the Use of Schools and Colleges

Stephen Chase - Algebra - 1849 - 348 pages
...b) 2 —a2—Zab +fi3 [ 11. N. 2.]. Hence, THEOR. II. The square of the difference of two numbers is equal to the sum of their squares, MINUS twice their product. See Geom. 183. Cor. vu. Multiply a — b by a — b, and see if the same formula results. 1. (x—...
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Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

Joseph Ray - Algebra - 1852 - 408 pages
...(2+5)2=4+20+25=49. ALGEBRAIC THEOREMS. 3 . (oa+iy) 2=aV+2 abxy+tfy*. 4. (ax2+3;i:z3)2 ART. 79. THEOREM II. — 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....
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - Algebra - 1848 - 250 pages
...a— 6 a2 — a6 — ab+V But a—b is the difference of tho quantities a and b ; hence THEOREM II. 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 tecond, plus the sqitare of the second....
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