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

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

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.

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

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

if (x)/(a^(2)-b^(2))=(y)/(b^(2)-c^(2))=(z)/(c^(2)-a^(2)) , then prove that x+y+z=0.

The sum of three expressions is x^(2)+y^(2)+z^(2) . If two of them are 4x^(2)-5y^(2)+3z^(2) and -3x^(2)+4y^(2)+2z^(2) then the third expression is

If (a^(2)+b^(2)+c^(2))(x^(2)+y^(2)+z^(2))=(ax+by+cz)^(2), then show that x:a=y:b=z:c

Let's apply, (a+b)^2 + (a-b)^2 = 2(a^2 + b^2) or (a+b)^2-(a -b)^2 =4ab or ab = (frac(a+b)(2))^2 - (frac(a-b)(2))^2 to find the following. Let's express 8x^2 + 50y^2 as the sum of two squares.