`(m+n) x+ (m-n) y=m^(2) -2mn-n^(2)` और `(m+n) (x+y)=m^(2) +n^(2),` जहाँ m ,n अचर है

Verify that (m + n) ( m ^(2) - mn + n ^(2)) = m ^(3) + n ^(3)

Simplify the following : (m-n)(m^(2)+mn+n^(2))

If (m + n)/(m + 3n) = (2)/(3) , find : (2n^(2))/(3m^(2) + mn) .

If m and n are distinct natural numbers, then which of the following is/are integer/integers? 1. (m)/(n) +(n)/(m) 2. mn ((m)/(n)+(n)/(m)) (m^(2)+n^(2))^(-1) 3. (mn)/(m^(2)+n^(2)) Select the correct answer using the code given below.

|[(m+n)^(2), l^(2), mn], [(n+l)^(2), m^(2), ln], [(l+m)^(2), n^(2), lm]| =(l^(2) +m^(2) +n^(2))(l-m)(m-n)(n-l)(l+m+n)

If m -n = 16 and m ^(2) + n ^(2) = 400, then find mn.

Factorise : 2(m^(2)+n^(2))^(2)-3mn(m^(2)+n^(2))-2m^(2)n^(2)

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

For the natural number m, n, if ( 1- y ) ^(m) (1 + y) ^( n) =1 + a _(1) y + a _(2) y ^(2) + ...+ a _( m + n) y ^( m +n) and a _(1) = a _(2) = 10, then the value of (m+n) is equal to :