Factorise the following expressions :
`(i) ax-ay+bx-by " " (ii) x^(2)-x-ax+a " " (iii) x^(4)+x^(3)+x^(2)+x`
`(iv) 16(a+b)^(2)-4a-4b " " (v) x^(2)+(1)/(x^(2))+2-3x-(3)/(x) " " (vi) x^(2)-((a)/(b)+(b)/(a))x+1`
`(vii) x^(2)+(a-(1)/(a))x-1 " " (viii)ab(x^(2)+y^(2)+xy(a^(2)+b^(2)) " "(ix) (ax+by)^(2)+(bx-ay)^(2)`

Factorise the following expressions: (i) x^(2) + 4x + 4 (ii) 3a^(2) -24ab+ 48b^(2) (iii) x^(5) -16x (iv) m^(2) +(1)/( m^(2)) -23 ( v) 6-216x^(2) (vi) a^(2) +(1)/( a^(2)) -18

Factorise the following : (i) 9a^(2)-b^(2) " " (ii) 81x^(3)-x " " (iii) x^(3)-49xy^(2) " " (iv) a^(2)-(b-c)^(2) (v) (x-y)^(3)-x+y " " (vi)x^(2)y^(2)+1-x^(2)-y^(2) " " (vii) 25(a+b)^(2)-49(a-b)^(2) " " (viii) xy^(5)-x^(5)y (ix) x^(8)-256 " " (x) x^(8)-81y^(8)

Factorise the following : (i) 9a^(2)-b^(2) " " (ii) 81x^(3)-x " " (iii) x^(3)-49xy^(2) " " (iv) a^(2)-(b-c)^(2) (v) (x-y)^(3)-x+y " " (vi)x^(2)y^(2)+1-x^(2)-y^(2) " " (vii) 25(a+b)^(2)-49(a-b)^(2) " " (viii) xy^(5)-x^(5)y (ix) x^(8)-256 " " (x) x^(8)-81y^(8)

Factorize each of the following expressions: a^(2)x^(2)+(ax^(2)+1)x+a3ax-6ay-8by+4bx

Factorize following expressions (i) a^2-4a+3+2b-b^2" (ii)" x^(4)+324" (iii)"x^4-y^2+2x^2+1 (iv) 4a^4-5a^2+1" (v)"x^6-7x^2-6

Factorize each of the following expressions: x^(2)-2ax-2ba+bx(2)x^(3)-2x^(2)y+3xy^(2)-6y^(3)abx^(2)+(ay-b)x-y(4)(ac+by)^(2)+(bx-ay)^(2)

Which of the following are polynomials ? (i) x^(2)-3x+1 " " (ii) x^(2)+5x+2 " "(iii) x-(1)/(y) " " (iv) x^(7)+8 " " (v) x^(3)+sqrt(x)-2 (vi) sqrt(2)x^(2)+x-1 " " (vii) (3x-1)(x+5) " " (viii) (x-(3)/(x))(x+2) " " (ix)2x^(2)-1 (x) x+(1)/(sqrt(x))+2

Which of the following are polynomials ? (i) x^(2)-3x+1 " " (ii) x^(2)+5x+2 " "(iii) x-(1)/(y) " " (iv) x^(7)+8 " " (v) x^(3)+sqrt(x)-2 (vi) sqrt(2)x^(2)+x-1 " " (vii) (3x-1)(x+5) " " (viii) (x-(3)/(x))(x+2) " " (ix)2x^(2)-1 (x) x+(1)/(sqrt(x))+2

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))

(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