`b^(2)c^(3)+8bc^(4)+12c^(5)`

Simplify : (2a+3b+4c) ( 4a^(2) + 9b^(2) + 16c^(2) -6ab - 12bc - 8ca )

if a , b , c and d are in proportion, prove that : (i) (a-b)/(c-d)= sqrt((3a^(2) + 8b^(2))/(3c^(2) + 8d^(2))) (ii) ((5a^(2) + 12c^(2))/(5b^(2) + 12d^(2))) = sqrt((3a^(4) - 7c^(4))/(3b^(4) - 7d^(4)))

If a,b, and c are in H.P.then th value of ((ac+ab-bc)(ab+bc-ac))/((abc)^(2)) is ((a+c)(3a-c))/(4a^(2)c^(2)) b.(2)/(bc)-(1)/(b^(2)) c.(2)/(bc)-(1)/(a^(2)) d.((a-c)(3a+c))/(4a^(2)c^(2))

Find the product (2a + 3b - 4c) (4a ^(2) + 9b ^(2) + 16 c ^(2) - 6 ab + 12 bc +8 ca)

If (a-2b-3c+4d)(a+2b+3c+4d) = (a+2b-3c-4d)(a-2b+3c-4d) then 2ad = "(a) 3bc (b) bc (c) 5bc (d) 2bc"

Find the product : (i) (a+2b+4c)(a^(2)+4b^(2)+16c^(2)-2ab-8bc-4ca) (ii) (3x-5y-4)(9x^(2)+25y^(2)+15xy+12x-20y+16) (iii) (2-3b-7c)(4+9b^(2)+49c^(2)+6b-21bc+14c) (iv) (sqrt(2)a+2sqrt(2)b+c)(2a^(2)+8b^(2)+c^(2)-4ab-2sqrt(2)bc-sqrt(2)ac)

Find the product : (i) (a+2b+4c)(a^(2)+4b^(2)+16c^(2)-2ab-8bc-4ca) (ii) (3x-5y-4)(9x^(2)+25y^(2)+15xy+12x-20y+16) (iii) (2-3b-7c)(4+9b^(2)+49c^(2)+6b-21bc+14c) (iv) (sqrt(2)a+2sqrt(2)b+c)(2a^(2)+8b^(2)+c^(2)-4ab-2sqrt(2)bc-sqrt(2)ac)

A (-1,4),B[1,-4) and C(5,4) are the vertices of a triangle.Then,the length of the altitude from A onto BC is (A) (12)/(5) (B) (12)/(sqrt(5)) (C) (12)/(5sqrt(5)) (D)3

If a+b+c=8 and ab +bc +ca =12 , then a^(3) +b^(3) +c^(3) -3abc is equal to :