(vi)((x)/(3)+(1)/(x))^(5)" (NCERT) "

Expand using binomial theorem: (i) (1-2x)^(4) " " (ii) (x+2y)^(5) (iii) (x-(1)/(x))^(6) " "(iv) ((2x)/(3)=(3)/(2x))^(5) (v) (x^(2) +(2)/(x))^(6)" "(vi) (1+(1)/(x^(2)))^(4)

(i) (3x^(2) +4x-5)/x (ii) ((x^(3) +1)(x-2))/x^(2) (iii) (x-4)/(2sqrtx) (iv) (( 1+x)sqrtx)/root3(x) (v) (ax^(2) +bx+c)/sqrtx (vi) (a+b cos x)/sin x

(vi) (2x ^ (2) - (1) / (x)) ^ (12)

Find each of the following products: (i) (x + 3) (x - 3) (ii) (2x + 5)(2x - 5) (ii) (8 + x)(8 - x) (iv) (7x + 11y) (7x - 11y) (v) (5x^(2) + (3)/(4) y^(2)) (5x^(2) - (3)/(4) y^(2)) (vi) ((4x)/(5) - (5y)/(3)) ((4x)/(5) + (5y)/(3)) (vii) (x + (1)/(x)) (x - (1)/(x)) (viii) ((1)/(x) + (1)/(y)) ((1)/(x) - (1)/(y)) (ix) (2a + (3)/(b)) (2a - (3)/(b))

which of the following expressions are polynomials ? Justify your answere, (i) 8 (ii) sqrt(3x)^(2)-2x (iii) 1-sqrt(5x) (iv) (1)/(5x^(-2))+5x+7 (v) ((x-2)(x-4))/(x) (vi) (1)/(x+1) (vii) (1)/(7)a^(3)-(2)/(sqrt(3))a^(2)+4a-7 (viii) (1)/(2x)

(i) (2x+3) (3x-5) (ii) x(1+x)^(3) (iii) (sqrtx + 1/x) (x -1/sqrtx) (iv) (x-1/x)^(2) (v) (x^(2) + 1/x^(2))^(3) (vi) (2x^(2) +5x-1) (x-3)

Which of the following expressions are polynomials ? In case of a polynomial , write its degree. (i) x^(5)-2x^(3)+x+sqrt(3) (ii) y^(3)+sqrt(3)y (iii) t^(2)-(2)/(5)t+sqrt(5) (iv) x^(100)-1 (v) (1)/(sqrt(2))x^(2)-sqrt(2)x+2 (vi) x^(-2)+2x^(-1)+3 (vii) 1 (viii) (-3)/(5) (ix) (x^(2))/(2)-(2)/(x^(2)) (x) root(3)(2)x^(2)-8 (xi) (1)/(2x^(2)) (xii) (1)/(sqrt(5))x^(1//2)+1 (xiii) (3)/(5)x^(2)-(7)/(3)x+9 (xiv) x^(4)-x^(3//2)+x-3 (xv) 2x^(3)+3x^(2)+sqrt(x)-1

Which of the following expression are polynomial .if not give reason : (i) (1)/( x^(2)) +3x -4 (ii) x^(2) (x-1) (iii) (1)/(x) (x+5) (iv) (1)/(x^(-2) ) +(1)/( x^(-1)) +7 (v) sqrt (5) x ^(2) + sqrt 3x +sqrt2 (vi ) m^(2) -3sqrt (m) +7m-10