If a²+b²+c² =16, and ab + bc + ca=10, find the value of a+b+c.

Simplify:

(i) (a+b+c)² +(a-b+c)²

(ii) (a+b+c)² -(a-b+c)²

(iii) (a+b+c)² +(a-b+c)²+(a+b-c)²

(iv) (2x+p+c)²-(2x-p+c)²

(v) (x²+y²-z²)²-(x²-y²+z²)²

If a+b+c =0 and a²+b²+c² =16, find the value of ab + bc + ca.

If a+b+c =9 and ab+bc+ca=23, find the value of a²+b²+c².

Find the value of 4x²+y²+25z²+4xy-10yz-20zx when x = 4, y = 3 and z = 2.