\fdO'^ - Old Forge Coal Mines

98 ALGEBRA.
In this case, where we are to subtract
2^— {'Sc -]-2d) —a from x, the result will be indicated by
x-[2d- {3c + 2d)-a.'] Ans. (Art. 408.)
(180) {a) 2x' -]- 2x' -{- 2x - 2
X -1
(c)
(d)
2x* + 2x' + 2x' - 2x
- 2x' - 2;ir' - 2^ + 2
2x* — 4x-\-2 Ans.
x^ — Aax -\- c
2x -{-
a
2x^ — Sax'' + 2cx
ax' — Aa'x + ac
2x' — lax' + 2^-*" — 4«'-«" + ac Ans.
- a*-irZa'b-2b*
6a' + ^ab
- ha" + 16a'b - IQa'b'
- %a'b + 21a'b' - ISab*
- ba" + Qa'k - lOa'b' + 21a'b' - ISab*
Arranging the terms according to the decreasing powers
of a, we have - ba" + %a'b + 21a' b' - 10a'b' - lSab\ Ans.
(181) (a) ^xyz
— Zxys
- 6xyz
The sum of the coefficients
of the positive terms we find to
be + 13, since (Sxyz
(+ 3) + (+ 6) +
(+4) = — %xyz
(+13).
When no sign is given before
"dxyz
— 4,xvz Ans
a quantity the -f sign must always
be understood. The sum
of the coefficients of the negative
terms we find to be — 17 since (— 9) + (— 5) + (— 3) =
(— 17). Subtracting the lesser sum from the greater, and
prefixing the sign of the greater sum ( — ) (Art. 390, rule
II), we have (+ 13) + (— 17) = — 4. Since the terms are
all alike, we have only to annex the common symbols xyz to
— 4, thereby obtaining — A:xyz for the result or sum.