`8a^3-(1)/(a^3) -2a+(2)/(a)`

If a-(1)/(2a)=3 , then the value of (a^(2)+(1)/(4a^(2)))(a^(3)-(1)/(8a^(3))) is

If the expression 2(1)/(2) of (3)/(4)xx(1)/(2)-:(3)/(2)+(1)/(2)-:(3)/(2)[(2)/(3)-(1)/(2) of (2)/(3)] is simplified,we get (a) (1)/(2) (b) (7)/(8)(c)1(5)/(8) (d) 2(3)/(5)

show that int (1)/((x^(2) + a^(2))^(3)) dx = (1)/(4a^(2)) (x)/((x^(2) + a^(2))^(2)) + (3)/(8a^(4)) (x)/(x^(2) + a^(2)) + (3)/(8a^(5)) tan^(-1) ((x)/(a)) + c

Factorise each of the following : (i) 8a^(3)+b^(3)+12a^(2)b+6ab^(2) (ii) 8a^(3)-b^(3)-12a^(2)b+6ab^(2) (iii) 27-125a^(3)-135a+225a^(2) (iv) 64a^(3)-27b^(3)-144a^(2)b+108ab^(2) (v) 27p^(3)-(1)/(216)-(9)/(2)p^(2)+(1)/(4)p

7(1)/(2)-((8)/(11)xx7(1)/(3))-:(3(1)/(2)-2(1)/(4))

Find the values of :- (1) (8)^(1//3) (2) (64)^(1//2) (3) 4^(5//2) (4) (36)^(3//2) (5) (27)^(2//3)

Find the values of :- (1) (8)^(1//3) (2) (64)^(1//2) (3) 4^(5//2) (4) (36)^(3//2) (5) (27)^(2//3)

Find the values of :- (1) (8)^(1//3) (2) (64)^(1//2) (3) 4^(5//2) (4) (36)^(3//2) (5) (27)^(2//3)

If |x| is so small that x^(2) and higher power of x may be neglected then the approximate value of ((4+x)^((1)/(2))+(8-x)^((1)/(3)))/((1-(2x)/(3))^((3)/(2))) when x=(6)/(25) is