Express `(1 + a^2)(1 + b^2)(1+c^2)` as the sum of two squares.

Express (1+a^(2))(1+b^(2)) as the sum of two squares.

Integers a,b,c satisfy a+b-c=1 and a^(2)+b^(2)-c^(2)=-1 What is the sum of all possible values of a^(2)+b^(2)+c^(2)?

Express A=[(1,-1,2),(2,1,3),(4,-1,5)] as a sum of a symmetric and a skew symmetric matrix

If the sum of the coefficients in the expansion of (b + c)^(20) {1 +(a -2) x}^(20) is equal to square of the sum of the coefficients in the expansion of [2 bcx - (b + c)y]^(10) , where a, b, c are positive constants, then

Express the matrix B=[2,-2,-4-1,3,41,-2,-3] as the sum of a symmetric and a skew symmetric matrix.

If |(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^2)|=0 and vectors (1,a,a^2),(1,b,b^2) and (1,c,c^2) are hon coplanar then the product abc equals (A) 2 (B) -1 (C) 1 (D) 0

Show that the points A(2, 1), B(0,3), C(-2, 1) and D(0, -1) are the vertices of a square.

On a graph paper, plot the points A(1, 1), B(1, 2), C(2, 1) and D(2, 2). Show that ACDB is a square.