Simplify `(m^2-n^2m)^2+ 2m^3n^2`

Simplify (7m-8n)^2+(7m+8n)^2

Simplify (4m+5n)^2+(5m+4n)^2

If m is the A.M. of two distinct real numbers l and n""(""l ,""n"">""1) and G1, G2 and G3 are three geometric means between l and n, then G1 4+2G2 4+G3 4 equals, (1) 4l^2 mn (2) 4l^m^2 mn (3) 4l m n^2 (4) 4l^2m^2n^2

Add the following: l^2 + m^2 , m^2+n^2 , 2lm+2mn+2nl

The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that a:b =(m+sqrt(m^2-n^2)):(m-sqrt(m^(2)-n^2)) .

If cosec theta- sin theta = m and sec theta - cos theta = n , prove that: (m^(2)n)^(2/3)+(n^(2)m)^(2/3)=1 .

The angle between the lines whose direction cosines satisfy the equations l+ m +n =0 and l^2= m^2 + n^2 is:

The equation of the line common to the pair of lines (p^(2)-q^(2)) x^(2)+(q^(2)-r^(2)) x y+(r^(2)-p^(2)) y^(2)=0 and (l-m) x^(2)+(m-n) x y+(n-l) y^(2)=0 is

Compute (3m -2n) ^(3)

If 'm' and 'n' are the roots of the equation x^(2) - 6x +2=0 , find the value of m^(3)n^(2)+n^(3)m^(2) :