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" No binomial can be a perfect square; for the square of a monomial is a monomial, and the square of a binomial is a trinomial. Thus... "
Elements of Algebra: For Colleges, Schools and Private Students - Page 148
by Joseph Ray - 1866 - 406 pages
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 376 pages
...the third term 4а6 is twice the product of the roots a and 2b; hence а is the root required. (153.) No binomial can be a perfect square. For the square...monomial is a monomial ; and the square of a binomial consists of three distinct terms which do not admit of being reduced with each other. Thus such an...
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 380 pages
...the squari? root of 9a2— 24o6 + 1662. Ex. 3. Find the square root of 9a4 — 30o36 + 25a262. (153.) No binomial can be a perfect square. For the square...monomial is a monomial ; and the square of a binomial consists of three distinct terms which do not admit of being reduced with each other. Thus such an...
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A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - Algebra - 1846 - 542 pages
...examples, however, very rarely occur. Before quitting this subject, we may make the following remarks: I. No binomial can be a perfect square ; for the square of a monomial is a monomial, and the square of the most simple polynomial, that is, a binomial, consists of three distinct terms, which do not admit...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 250 pages
...x+ia. 14. x2— 2x+l+2xy— 2y-\-y2 Ans. x+y— 1. 15. x(x+l)(x+2)(x+3) + l Ans. x2+3x+l. ART. 197. — The following remarks will be found useful. 1st. No...a2+62 is not a perfect square ; but if we add to it 2ab, it becomes the square of 0+6 ; and subtracting from it 2ab, it becomes the square of o — b....
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 252 pages
...x(x+l)(x+2)(x+3) + l Ans. x2+3x+l. ART. 197. — The following remarks will be found useful. 1st. Aro binomial can be a perfect square; for, the square...and the square of a binomial is a trinomial. Thus, a*+6* is not a perfect square; but if we add to it 2a6, it becomes the square of a+6 ; and subtracting...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - Algebra - 1848 - 250 pages
...x+^a. 14. z2— 2z+l+2xy— 2y+^ Ans. x+y— 1. 15. x(x+l)(x+2)(x+3) + l Ans. r*+3z+l ART. 19H* — The following remarks will be found useful. 1st. No...square of a monomial is a monomial, and the square of a binffmial is a trinomial. Thus, a?-\-V is not a perfect square; but if we add to it 2ab, it becomes...
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A Treatise on Algebra

Elias Loomis - Algebra - 1855 - 356 pages
...Ex. 3. Find the square root of 9a4— 30a'6+25aW. Ex. 4. Find the square root of 4a'+14a6+96'. (153.) No binomial can be a perfect square. For the square...monomial is a monomial ; and the square of a binomial consists of three distinct terms, which do not admit of being reduced with each other. Thus such an...
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The Elements of Algebra

Elias Loomis - Algebra - 1856 - 280 pages
...;-u*ult obtiiuod be verified f I Ex. 10. Required the square root of the polynomial Am. a'+a'+a+1. (157.) No binomial can be a perfect square. For the square...monomial is a monomial ; and the square of a binomial consists of three distinct terms, which do not admit of being reduced to a less number. Thus the expression...
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Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

Joseph Ray - Algebra - 1857 - 408 pages
...square roots of a;2+a2, and of a:2— 2ax. . , , • Ans. x-}- ---- ---- + fee. ^' ' &, _______ AKT. 184. The following remarks will be found useful. 1st....square, but if we add to it, or subtract from it, 2ab, it becomes the square of a-|-6 or of a — b. 2nd. In order that a trinomial may be a perfect...
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A Course of Mathematics: Composed for the Use of the Royal Military Academy

Charles Hutton - Mathematics - 1860 - 1014 pages
...examples however very rarely occur. Before quitting this subject we may make the following remarks : — L No binomial can be a perfect square ; for the square of a monomial is i monomial, and the square of the most simple polynomial, that is, a binonii.il, consists of three...
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