Page:Elementary algebra (1896).djvu/25

given, and by combining the terms the numerical value of the whole expression is obtained.

16. We have already, in Art. S 8, called attention to the importance of carefully distinguishing between coefficient and index; confusion between these is such a fruitful source of error with beginners that it may not be unnecessary once more to dwell on the distinction.

{{fine block|Ex. 1. When $c=5$, find the value of $c^{4}-4c+22c^{3}-3c^{2}$.

Here

${\begin{aligned}c^{4}&=5^{4}=5\times 5\times 5\times 5\times 5=625\\4c&=4\times 5=20\\2c^{3}&=2\times 5^{3}=2\times 5\times 5\times 5=250\\3c^{2}&=3\times 5^{2}-3\times 5\times 5=75\end{aligned}}$

Hence the value of the expression $=625-20+250-75=780$.

Ex. 2. When $p=9$, $r=6$, $k=4$, find the value of

${\frac {1}{3}}{\sqrt[{3}]{\left({\frac {pr}{k^{2}}}\right)}}+{\sqrt {(3k+k^{3}+5)}}-{\frac {2r^{2}}{9k}}$.

${\begin{aligned}{\frac {1}{3}}{\sqrt[{3}]{\left({\frac {pr}{k^{2}}}\right)}}+{\sqrt {(3k+k^{3}+5)}}-{\frac {2r^{2}}{9k}}&={\frac {1}{3}}{\sqrt[{3}]{\left({\frac {54}{16}}\right)}}+{\sqrt {(12+64+5)}}-{\frac {2\times 36}{9\times 4}}\\&={\frac {1}{3}}{\sqrt[{3}]{\frac {27}{8}}}+{\sqrt {81}}-2\\&={\frac {1}{3}}\times {\frac {3}{2}}+9-2=7{\frac {1}{2}}\end{aligned}}$

17. By Art. 13 any term which contains a zero factor is itself zero, and may be called a zero term.

Ex. 1. If $a=2$, $b=0$, $x=3$, $y=1$, find the value of

$4a^{3}-ab^{3}+2xy^{2}+3abx$

The expression

${\begin{aligned}&=(4\times 2^{3})-0+(2\times 3\times 1)+0\\&=32-0+6+0=38\end{aligned}}$

Note. The two zero terms do not affect the result.

Ex. 2. Find the value of ${\frac {3}{5}}x^{2}-a^{2}y+7abx-{\frac {5}{2}}y^{3}$, when

$a=5$, $b=0$, $x=7$, $y=1$.

${\begin{aligned}{\frac {3}{5}}x^{2}-a^{2}y+7abx-{\frac {5}{2}}y^{3}&={\frac {3}{5}}\times 7^{2}-5^{2}\times 1+0-{\frac {5}{2}}\times 1^{3}\\&=29{\frac {3}{5}}=25-2{\frac {1}{2}}=1{\frac {9}{10}}\end{aligned}}$

Note. The zero term does not affect the result.

18. In working examples the student should pay attention to the following hints:

1. Too much importance cannot be attached to neatness of style and arrangement. The beginner should remember that neatness is in itself conducive to accuracy.