Factors of x² + 4y² + 4y − 4xy − 2x − 8
The factors of \[ x^2+4y^2+4y-4xy-2x-8 \] are
(a) \((x-2y-4)(x-2y+2)\)
(b) \((x-y+2)(x-4y-4)\)
(c) \((x+2y-4)(x+2y+2)\)
(d) none of these
Solution
\[ x^2+4y^2+4y-4xy-2x-8 \]
\[ =x^2-4xy+4y^2-2x+4y-8 \]
\[ =(x-2y)^2-2(x-2y)-8 \]
Let \[ z=x-2y \]
\[ =z^2-2z-8 \]
\[ =(z-4)(z+2) \]
\[ =(x-2y-4)(x-2y+2) \]
Therefore,
\[ \boxed{(a)\ (x-2y-4)(x-2y+2)} \]