\fdO'^ - Old Forge Coal Mines

96 ALGEBRA.
(171)
See Arts. 352 and 353.
(172) («) In the expression 4:xy — 12;try -|- Sxy"", it is
evident that each term contains the common factor ixjf.
Dividing the expression by 4-ry, we obtain x'' — 3xy -f 2^
for a quotient. The two factors, therefore, are 4a-j and
;r' - Sxy + 2f\ Hence, by Art. 452,
4;ir'y - 12;iry + 8;i'j>^' = ixyix" - 34r> + 2/). Ans.
(^) The expression {x* —y*) when factored, equals {x'' -j-
/)(-^' -/). (Art. 463.) But, according to Art. 463, r^
—y may be further resolved into the factors (x -\-j^){x — /).
Hence, {x* — y) = (^' +y )(•*'+/)(*' —j)- Ans.
(^) Sx' — 27/. See Art. 466. The cube root of the
first term is 2x, and of the second term is 3/, the sign of the
second term being — . Hence, the first factor of Sx^ — 27j'
is 2x — Sf. The second factor we find to be 4;jr* + ^-^f + 9j'»
by division. Hence, the factors are 2x — 3/ and
4;ir' + 6xy + 9^".
(173)- Arranging the terms according to the decreasing
powers of m.
3m' + lOm^n + lO^nn^ + dn'
dm*n — 5m'n'' + dfw'n' — mn^
^nfn + 307«"«" + 30;«';«=' + %m'n*
— Um'n^ — 50m'n' — 50m'n* — 15m'n*
4- 15m^n' + oOm*n* + 507;/'«' + 15m'n*
— dm*n* — 10 ///' ;?^ — IQjM'fi' — 3mn'
%m'n + ISw'w" — 5/«*«* 4- 6»2'«* + 25;«'«' + 5w'«' — 3w«'
Ans.
(174) {2a'bcy = lQa'b*c'\ Ans.
( - 3«'^V)^= - 243a"'