...radical sign is <"c8 sin.2 0 cos.2 0' + *2e2 sin.2 0' cos.2 0, and the sum just mentioned is evidently equal to twice the product of the square roots of these terms. Thus the whole quantity under the radical sign is the square of the binomial tc (sin. 0 cos. 0' + cos....

...is necessarily a surd, and a binomial always becomes a radical by evolution. (2). III. A trinomial is a perfect square when two of its terms are perfect squares and positive, and the remaining term is twice the product of the square roots of the others, and either...

...monomial is a monomial, and the square of the least polynomial is a trinomial. NOTE 3. — A trinomial is a perfect square when two of its terms are perfect...the remaining term is equal to twice the product of their square roots. For, (a — J)' = a* Therefore the square root of a3 ± 2 ab -\- W is a ± 6. Hence,...

...root of 4z2 — 12zu/ -f- 9¿/2. This is a perfect square, because 4z2 and 9«/2 are squares, and 12zy is equal to twice the product of the square roots of these terms. The square root of 4z2 is 2z, and the square root of 9z/2 is 3y. Connecting these results by the sign of...

...is necessarily a surd, and a binomial always becomes a radical by evolution. (2). III. A trinomial is a perfect square when two of its terms are perfect squares and positive, and the remaining term is twice the product of the square roots of the others, and either...

...polynomial with the least number of terms, that is, of a binomial, is a trinomial. NOTE 3. — A trinomial is a perfect square when two of its terms are perfect...the remaining term is equal to twice the product of their square roots. For, (a + b)* = a" -\-2ab-\-V (a — 6)2 = a2 — ïab + V Therefore the square...

...= — to find x. (•) i— vi— x* i+vi— x* * (/i) By discussion of the principle, "A trinomial is a perfect square when two of its terms are perfect squares and positive, and the third term is twice the product of their square roots, and either positive or negative,"...

...b + 9 V = (2 а - 3 b) (2 а — 3 b), since (2а-35)2 = 4a2-12а5 + 962 [Р. 32]. 98. A trinomial is a perfect square when two of its terms are perfect squares, and the other term is ± twice the square root of their product. 1. ж3 - f il. а6 + 1 21. a^ + / 2. x3 -(-...

...^629.38+. REVIEW. Page 289. 14. Since the first and third terms are perfect squares, and the second term is equal to twice the product of the square roots of the other terms, the expression is aperfect square. Hence, the factors are (2x+y)'(2x+y). 15. Since...

...coefficients of two of the terms have like signs and are perfect squares. Then, see if the coefficient of the remaining term is equal to twice the product of the square roots of the coefficients of the other two terms. Lastly, extract the square root of those two terms whose coefficients...