Page:Elementary algebra (1896).djvu/515

497 Rh 12. Subtract - x^2 + y^2 - z^2 from the sum of {1}{3}x^2 + {1}{4}y^2, {}{5}y^2 +{1}{3}z^2, and {1}{3}z^2 - {1}{4}x^2, 13. Write the cube of x+ 8y. 15. Solve {3}{5}(2x-7)-{2}{3}(x-8)= {4x+1} {15} + 4.

14. Simplify {x^2+xy}{x^2+y^2}{x^4 -y^4}{x+ y^2}{y}{x}

16. Find the H.C.F. and L. C. M. Ma x^4+x^3+2x-4 and x^3+ 3x^2-4. 17. Find the square root of 4a^4+9(1 -2a)+3a^2(7 - 4a).

18. Solve y = {x+a}{2} + {b}{3}\\ x = {y+b}{2} + {a}{3}

19. Simplify ({a}{x+a} - {x}{x-a}) {x^2+a^2}{x^2+ax}. 20. When 1 is added to the numerator and denominator of a certain fraction the result is equal to 3; and when 1 is subtracted from its numerator and denominator, the result is equal to 2: find the fraction.

21. Show that the sum of 12a+6b-c, -7a-b+c and a+b+6c, is six times the sum of 25a+13b-8c, -18a-18b-c, and -11a+b+10c.

22. Divide x^2 - xy + {3}{16}y^2 by {14}{}y.

23. Add together 24. Find the factors of (i.) 10x^2+79x-8. (ii.) 729x^6 - y^6.

25. Solve : {2x-1}{5} + {5x+3}{17} = 3 - {4x-118}{11}.

26. Find the value of (5a-3b)(a-b)-b{3a -c(4a-b)- b^2(a+c)}, when a=0, b=- 1, c={1}{2}. 27. Find the H.C. F. of 72x^3-10x^2-7x+10 and 2 x^3-x^2-2x+1.

28. Simplify {x^2-7xy +12 y^2}{x^2+ 5xy + 6y^2 } {x^2- 5xy + 4y^2}{x^2+ xy -2y^2}