[" Pactorise the following."],[" (i) "ab(x^(2)+1)+x(a^(2)+b^(2))(" ii ")]

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

factorize : ab(x^2+1)+x(a^2+b^2)

What is the lowest common multiple of ab (x^(2)+1) + x (a^(2)+b^(2)) and ab (x^(2)-1) + x(a^(2)-b^(2)) ?

Factorise the difference: (i)3-12(a-b)^(2)(ii)1-2ab-(a^(2)+b^(2))

Verify Rolle's theorem for the following functions (i) f(x) = sqrt(4 - x^(2)) " in " [-2, 2] (ii) f(x) = log ((x^(2) + ab)/((a + b)x)] " in " [a, b], " where " 0 lt a ltb

Try do draw the geometrical figure for following identities. (i) (x +y) ^(2) -= x ^(2) + 2xy + y^(2) (ii) (x +y) (x-y) -=x ^(2) -y ^(2) (iii) (x +a) (x+b) -=x ^(2) + (a+b) x +ab (iv) (x+a) (x+b) (x+c) -=x ^(3) + (a+b+c)x ^(2) + (ab + bc + ca)x + abc

Find the LCM of the polynomials ab(x^(2)+1)+x(a^(2)+b^(2)) and ab(x^(2)-1)+x(a^(2)-b^(2))

Find the product of the following binomials; (i) (2x+y)(2x+y) (ii) (a+2b)(a-2b)