Factor (x^(2)+4xy+16y^(2))

Question

this is for a college class

Answer 1

x²+4xy+16y² has only complex factors. To find them:

x²+4xy+16y²=0,

x²+4xy=-16y², add 4y² to bothe sides to complete the square on the LHS:

x²+4xy+4y²=4y²-16y²=-12y²,

(x+2y)²=-12y²,

(x+2y)²+12y²=0,

(x+2y+2iy√3)(x+2y-2iy√3)=0, so x=-2y±2iy√3=2y(-1±i√3).