Factoring an expression

Question

I want to prove that $$[2b^2-c(b+c)][2c^2-b(b+c)]\leq0$$ when $$ bc\leq0$$ but i don't have any clue on how to factor that expression. I tried multiplying the terms within the paranthesis but all that i got was a mess.

Answer 1

Hint:

$$2x^2-xy-y^2=2x(x-y)+y(x-y)=?$$

Answer 2

i have your term factorized in the form $$-(c-b)^2 (2 b+c) (b+2 c)$$