An inequality for a tow variable function

Suppose that ##F(u,v)=a|u+v|^{r+1}+2b|uv|^{\frac{r+1}{2}}##, where ##a>1, b>0## and ##r\geq3.## How we can show that there exists a positive constant c such that

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F(u,v)\geq c\Big( |u|^{r+1}+|v|^{r+1}\Big).

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