Answer
$2(x^{2}+4)^{4}(x-2)^{3}(7x^{2}-10x+8)$
Work Step by Step
$5(x^{2}+4)^{4}(2x)(x-2)^{4}+(x^{2}+4)^{5}(4)(x-2)^{3}$
Take out common factor $(x^{2}+4)^{4}(x-2)^{3}$:
$(x^{2}+4)^{4}(x-2)^{3}[5(2x)(x-2)+(4)(x^{2}+4)]=...$
Simplify:
$...=(x^{2}+4)^{4}(x-2)^{3}[10x(x-2)+4x^{2}+16]=...$
$...=(x^{2}+4)^{4}(x-2)^{3}(10x^{2}-20x+4x^{2}+16)=...$
$...=(x^{2}+4)^{4}(x-2)^{3}(14x^{2}-20x+16)=...$
Finally, take out common factor $2$ from the third parentheses:
$...=2(x^{2}+4)^{4}(x-2)^{3}(7x^{2}-10x+8)$
