Expand `5sqrt5` in increasing power of `4/5`

Expand 3sqrt3 in increasing power of 2/3

If (x-4)/(x^(2)-5x+6) can be expanded in the ascending powers of x , then the coefficient of x^(3) is

Expand (2+ x)^(5) - (2- x)^(5) in ascending powers of x and simplify your result.

Expand (1+4x)^(5) .

Expand (2x + 5y)^(5)

The simplest rationalising factor of 2sqrt(5)-sqrt(3) is (a) 2sqrt(5)+\ 3 (b) 2sqrt(5)+sqrt(3) (c) sqrt(5)+sqrt(3)\ \ (d) sqrt(5)-sqrt(3)

Expand: (4a- 5b- 2c)^(2)

Without expanding, show that the value of each of the following determinants is zero: |(sqrt(23)+sqrt(3),sqrt(5),sqrt(5)),(sqrt(15)+sqrt(46),5,sqrt(10)),(3+sqrt(115),sqrt(15),5)| .

If a+bsqrt(5)=(4-3sqrt(5))/(4+3sqrt(5)) , then find the values of a and b.

If (4+3sqrt5)/(4-3sqrt5)=a+bsqrt5 ,a, b are rational numbers, them (a, b)=