Factorise : `a^3(1+m)^3-((a l)/3+(2a m)/3)^3-((2a l)/3+(a m)/3)^3.`

Factorise : 2l^3+432m^3

Factorise: 2m^2+5m-3

Resolve into factors : (5l-2m)^3+(m-2n)^3+(m+2n-5l)^3

Dimensions of epsilon_(0) are M^(-1)L^(-3)T^(4)A^(2) M^(0)L^(-3)T^(3)A^(3) M^(-1)L^(-3)T^(3)A M^(-1)L^(-3)TA^(2)

1m^(3) = ? L

Show that the matris [[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]] is orthogonal, if l_(1)^(2) + m_(1)^(2) + n_(1)^(2) = Sigmal_(1)^(2) = 1 = Sigma l_(2)^(2) = Sigma_(3) ^(2) and l_(1) l_(2) + m_(1)m_(2) + n_(1) n_(2) = Sigma l_(1)l_(2) =0 = Sigma l_(2)l_(3) = Sigma l_(3) l_(1).

Find the product : (9m -2 l)(4l -3 m)

Show that the condition that tha concurrent lines with direction cosines (l_(1).m_(1),n_(1)),(l_(2),m_(2),n_(2))and(l_(3),m_(3),n_(3)) are coplanar is l_(1)(m_(2)n_(3)-m_(3)n_(2))+m_(1)(n_(2)l_(3)-n_(3)l_(2))+n_(1)(l_(2)m_(3)-l_(3)n_(2))=0