Inequation / binomial formula

Question

I have the following inequation: $ (-av-w sinu + b)^2 \leq 3(a^2v^2 + w^4 u^4+b^2)$ How does this work. Maybe I have to use: $2uv \leq u^2+v^2$? Can somebody explain this to me?

Answer 1

Hint: Expanding the left-Hand side we obtain: $$a^2 v^2-2 a b v+2 a v w \sin (u)+b^2-2 b w \sin (u)+w^2 \sin ^2(u)$$