Question

Descompuneti in factori 4x^2+9y^2+12xy-4x-6y-8

Answer 1

$4x^2+9y^2+12xy-4x-6y-8=\\(4x^2+12xy+9y^2)-2(2x+3y)-8=\\(2x+3y)^2-2(2x+3y)-8=\\2x+3y\stackrel{not}{=} t . \text{Atunci:}\\t^2-2t-8 =t^2-4t+2t-8 = t(t-4)+2(t-4)=(t-4)(t+2)\\=\boxed{(2x+3y-4)(2x+3y+2)}$