Question

factorize: x²+4y²-5x+10y-4xy+6​

Answer 1

Answer:

(x-2y-2)(x-2y-3)

Step-by-step explanation:

$x^{2} +4y^{2} -5x+10y-4xy+6\\=(x^{2}-4xy+4y^{2})-5x+10y+6\\=(x-2y)^{2} -5(x-2y)+6$

Let x-2y = a

hence above equation becomes,

$=a^{2}-5a+6\\=a^{2} -2a-3a+6\\=a(a-2)-3(a-2)\\=(a-2)(a-3)$

substitute back the value of a=z-2y, we get,

$(a-2)(a-3)\\=(x-2y-2)(x-2y-3)$