SOH7T10NS TO THE EXERCISES.] M ATHEM ATICS. ALGEBR A. 



491 



6. (2o s 4x 9 5xy") X 3ax"y = 6a 3 4x 4 y 



7. (2axy* 3x"z -f 2x) X 4axy = 8a" j- 



8ax 2 y. 



8. (avry 1 + 3ny 2 Zy 3 *) X 6m 2 x*y = 6m Vy 4 



9. (4yV 3az> Sty 3 ) X 5ai 2 y = 20a4 2 



+ 15a=4 !; 

 10. (5C* V yV 3z 4 ) 12 



11. (5ar J4y 2 2c2 J ) X 12a 2 ie 3 = 



+ 3a 2 4Vy" + 24a ! 4c 4 z. 



12. {4fly (2i'z* yz 2)} Za'yz' [iay* 24z 3 + yz 

 + 2} Sa'yz 3 = 12a 3 y V fci'i'y** + 3a'y V+ Ga'yi 3 . 



13. {24jrV (5cy'r + 4yz 3 3r')} X 3j:-y = 



X 3-r 2 y = 



14. 



+ ea' 



cy')} X 2a-4Vy = 

 "y 3 } X - 2a-4- xy = 

 a'4=j j y ga'i^y'. 



McmriJCATiox. CASK III. PAGE 461. 



34J- 2 

 3x 2x 



tax* + C4x= -f Ax 



(4a + 94) x 3 + C(4 



2. 4oy + '&bx 4e 

 34y + 2c 



12a4y' + 94' xy I2tey 



8acy + dbcx 8c' 



12a4y + (94'or 



2y) 8c'. 



3. 5x* 4.r 5 + 3x 2 

 2x 3 x + 1 



lOj- 5 8^ 4 4- Or 3 4 jr 3 



5^' -1- 4a- 3 3^ J + 2r 



5x" 4i -j- 3i 2 



2. 



4. 



2) = *' 4; 

 * 9 



: 3) = ** 9 



9x + 36 

 x' 13x + 36.* 



5. (x + a)(x a) = x' a 3 ; (x 1 a')(a* a 5 ) 



= r 4 2a'x 5 4 a 4 . 

 C. 2x 4- 3a 

 4x 5a 



lOax 15a* 



15a 



15a 



lOaj* 13aj 15a 3 . 



7. Sax 4 



12aV 4a4x 



3acx be 



12aV + (3c 44)aj 4c 



tar I 



GOaV + 5(3e 44)aV 



36aV 3(3c 44)aj- + 34e 



GOa V + {5(3c 44) 36} a"x* {3(3c 44) + 54c} ax + 34c. 



8. 4ax + 34y 1 

 2aj 4y + 2 



6a4xy 2ax 

 4a4xy 34 7 y 5 -\- by 



Sax + 64y 2 



Sa'x 3 + 2a4jy + Gax 34-y 1 + 'by 2. 



9. (X - y) 3 (x + y) = (x - y)*( _ y)( x + y) = (, _ y)!(* _ yl) 



x 3 - 2xy + y' 



x 4 2x 3 y + 2xy* y 4 . 



10. x' (a -f 4)x + c 

 x c 



x 3 (a 4- 4)x 4 ex 



fx 3 4 (a 4- 4)cx c' 



x 3 (a + 4 4 c)x 3 4 (a 4. 4 + l)cx , 



1 1 . 3 3 (x 5 a"-)"- = 2 l(x* 2aV + a 4 . 



12. (2x + 3)(2jr 3)(4x' + 9) = 4x 2 9)(4x' + 9) = 16x 4 81. 



13. { (x + 2)(* 2)} 2 = (x' 4)' = * 4 8x + 16.f 



See Algebra, p. 460. t 8c ante, p. 400. 



