Find the value

$(x+2)\left(x^{2}+25\right)-10 x(x+2)$

Taking (x + 2) common in both the terms

$=(x+2)\left(x^{2}+25-10 x\right)$

$=(x+2)\left(x^{2}-10 x+25\right)$

Splitting the middle term of $\left(x^{2}-10 x+25\right)$

$=(x+2)\left(x^{2}-5 x-5 x+25\right)$

$=(x+2)\{x(x-5)-5(x-5)\}$

$=(x+2)(x-5)(x-5)$

$\therefore(x+2)\left(x^{2}+25\right)-10 x^{2}-20 x=(x+2)(x-5)(x-5)$