Solution:

\((x^3+\frac{4}{x^2})^4=((x^3+\frac{4}{x^2})^2)\)

\(=(x^6+\frac{16}{x^4}+8x)^2\)

\(=x^{12}+\frac{256}{x^8}+64x^2+2[x^6\cdot\frac{16}{x^4}+x^6\cdot8x+\frac{16}{x^4}\cdot8x]\)

So: \((a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ac)\)

Required form =8x

Coefficient \(x^2=8\)

\((x^3+\frac{4}{x^2})^4=((x^3+\frac{4}{x^2})^2)\)

\(=(x^6+\frac{16}{x^4}+8x)^2\)

\(=x^{12}+\frac{256}{x^8}+64x^2+2[x^6\cdot\frac{16}{x^4}+x^6\cdot8x+\frac{16}{x^4}\cdot8x]\)

So: \((a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ac)\)

Required form =8x

Coefficient \(x^2=8\)