Page:Elementary algebra (1896).djvu/111

93 Rh 7. 4a2b3c2, 6 a3b2c3. 12. 25xy2z, 100 x2yz, 125 xy.

8. 7a2b4c5, 14 ab2c3. 13. a2bpxy, b2qxy, a3bxr2.

9. 49 ax2, 63 ay2, 56 az2. 14. 15 a5b3c7, 60 a3b7c6, 25 a4b5c2.

10. 17 abc, 34a2bc, 51 abc2. 15. 35 a2c3b, 42 a3cb2, 30 ac2b3.

11. a3x2y2, b3xy2, c3x2y. 16. 24 a3b2c3, 16 a3b4c2, 40 a2b3c5.

COMPOUND EXPRESSIONS.

113. H.C. F. of Compound Expresans which can be factored by Inspection. The method employed is similar to that of the preceding article.

Ex. 1. Find the highest common factor of

4 cx3 and 2 cx3 + 4c2x2.

It will be easy to pick out the common factors if the expressions are arranged as follows :

4 cx3 = 4cx3, 2 cx3 + 4 c2x2 = 2 cx2(x +2c);

therefore the H.C. F. is 2 cx2.

Ex. 2. Find the highest common factor of 3a2+ 9ab, a3 — 9ab2, a3+ 6 a2b + 9ab2.

Resolving each expression into its factors, we have

3a2+9ab=3a(a+ 3b), a3 —9ab2 =a(a+3b)(a— 3b), a3+ 6a2b + 9ab2 =a(a+ 3b)(a+ 3b);

therefore the H.C. F. is a(a+3b).

114. When there are two or more expressions containing different powers of the same compound factor, the student should be careful to notice that the highest common factor must contain the highest power of the compound factor which is common to all the given expressions.

Ex. 1. The highest common factor of a(a—x)2, a(a— x)2, and 2ax(a— x)5 is (a — x)2.

Ex. 2. Find the highest common factor of ax2 + 2 a2x + a3, 2ax2 — 4 a2x — 6a3, 3(ax+ a2)2.