" (i) "(x+2y+4z)^(2)quad " (ii) "(2x-

Expand each of the following, using suitable identities : (i) (x+2y+4z)^(2) (ii) (2x-y+z)^(2) (iii) (-2x+3y+2z)^(2) (iv) (3a-7b-c)^(2) (v) (-2x+5y-3z)^(2) (vi) [(1)/(4)a-(1)/(2)b+1]^(2)

Expand each of the following, using suitable identities: (i) (x+2y+4z)^2 (ii) (2x-y+z)^2 (iii) (-2x+3y+2z)^2 (iv) (3a-7b-c)^2 (v) (-2x+5y-3z)^2 (vi) [1/4a-1/2b+1]^2

Expand each of the following , using suitable identities : (i) (x+2y+4z)^2 (ii) (2x-y+z)^2 (iii) (-2x+3y+2z)^2 (iv) (3a-7b-c)^2 (v) (-2x+5y-3z)^2 (vi) (1/4a-1/2b+1)^2

Expand each of the following, using suitable identities: (i) (x+2y+4z)^2 (ii) (2x-y+z)^2 (iii) (-2x+3y+2z)^2 (iv) (3a-7b-c)^2 (v) (-2x+5y-3z)^2 (vi) [1/4a-1/2b+1]^2

If x = 1, y = 2 and z = 5, find the value of (i) 3x - 2y + 4z (ii) x^(2) + y^(2) + z^(2) (iii) 2x^(2) - 3y^(2) + z^(3) (iv) xy + yz - zx (v) 2x^(2) y - 5yz + xy^(2) (vi) x^(3) - y^(3) - z^(3)

Find the following products: (i) (z^2+2)(z^2-3) (ii) (3x-4y)(2x-4y) (iii) (3x^2-4x y)(3x^2-3x y) (iv) (x+1/5)(x+5)

|[y+z, x, x] , [y, z+x, y] , [z, z, x+y]|= (i) x^2y^2z^2 (ii) 4x^2y^2z^2 (iii) xyz (iv) 4xyz

Show that the lines : (i) (x -5)/(7) = (y + 2)/(-5) = (z)/(1) " " and (x)/(1) = (y)/(2) = (z)/(3) (ii) (x - 3)/(2) = (y + 1)/(-3) = (z - 2)/(4) and (x + 2)/(2) = (y - 4)/(4) = (z + 5)/(2) are perpendicular to each other .

If sin ^ (- 1) x + sin ^ (- 1) y + sin ^ (- 1) z = pi show that, x ^ (4) + y ^ (4) + z ^ (4) + 4x ^ ( 2) y ^ (2) z ^ (2) = 2 (x ^ (2) y ^ (2) + y ^ (2) z ^ (2) + z ^ (2) x ^ (2))