Question # 01: Factorize each of the following expressions:
\((iii)\) \(\;\) \(x^4+4x^2+16 \)
Solution:
\(\ \ \ \ x^4+4x^2+16\)
\(=(x^{2})^2 +4x^{2} +16+4x^{2} -4x^{2}\)
\(=(x^{2})^2 +8x^{2} +16-4x^{2}\)
\(=(x^{2})^2 +2\left( x^{2}\right)( 4) +( 4)^{2} -4x^{2}\)
\(=( x^2+4)^{2} -( 2x)^{2}\)
\(=( x^2+4+2x)( x^2+4-2x)\)