\fdO'^ - Old Forge Coal Mines

ALGEBRA. y7
{c) 16x* — Sx*y* + xy*, when factored =
(4.r» - xy'){Ax' - xy^). (Art. 467, Rule.)
But, (4a-' - ;r/) = ^'(2^ + j)(2;r - j). (Arts. 462 and
463.)
Hence, 16^* - 8;try + .ry= .r" (2^ + j) (2;r + j) {2x — y)
{}lx — y).
(176)
4a* — 3a\r
Ans.
4a'— 6a'jr—a^
4a' - 12^^ +5«*.r»+6a';r*+aV(2a='-3aV-a4r*
4a* Ans.
— 12a'^ + ha*x
- 12a'x + QaV"
— 4a'jr* + 6a'.r' + a';ir*
— 4a*;tr' + 6a';ir' + aV
(177) (a) 6a*/^^ + a*^'-7a»/^» + 2a(5^ + 8.
{d)
3 + 2a/^c + a'd' - 7a'd' + 6a^^\
(c) 1 + a^ + a" + 2 a'. Written like this, the a in the
second term is understood as having 1 for an exponent;
hence, if we represent the first term by a", in value it will
be equal to 1, since a" = 1. (Art. 439.) Therefore, 1
should be written as the first term when arranged according
to the increasing powers of a.
(178) i^lGa^W? = ± 2a'dc\ Ans. (Art. 621.)
V-32a"= - 2a'. Ans.
f/-l,728aV"jry = - 12aV*Ay. Ans.
(179) (a) {a-2x-^4y)-{32+2d-c). Ans. (Art. 408.)
{d) —^b — A:C-{-d— (2/— Ze) becomes
_ [3^ _[- 4^ _ ^-|- (2/— 3f)J when placed in brackets pre-
ceded by a minus sign. Ans. (Art. 408.)
[c) The subtraction of one expression or quantity from
another, when none of the terms are alike, can be represented
only by combining the subtrahend with the minuend
by means of the sign — .