Prove that `^10P_3=^9P_3+3.^9P_2`

Prove that (1)8P_(3)=7P_(3)+3.7P_(2) and (2)9P_(4)+4.9P_(4)=10P_(4)

Prove that ""^(9)P_(3)+3xx""^(9)P_(2)=""^(10)P_(3).

Prove that : (i) ""^(n)P_(n)=2""^(n)P_(n-2) (ii) ""^(10)P_(3)=""^(9)P_(3)+3""^(9)P_(2) .

"is"^(10)P_(3)= ""^(9)P_(2)+3""^(9)P_(3) ?.

If p_(2),p_(2),p_(3) are the perpendiculars from the vertices of a triangle to the opposite sides, then prove that p_(1)p_(2)p_(3)=(a^(2)b^(2)c^(2))/(8R^(3))

Find r if : ^10P_r=2. ^9P_r

If (1-x+x^(2))^(4)=1+P_(1)x+P_(2)x^(2)+P_(3)x^(3)+...+P_(8)x^(8) , then prove that : P_(2)+P_(4)+P_(6)+P_(8)=40 and P_(1)+P_(3)+P_(5)+P_(7)=-40 .

If p=2-a, prove that a^(3)+6ap+p^(3)-8=0

If p=2-a; prove that a^(3)+6ap+p^(3)-8=0