Question # 01: Factorize each of the following expressions:
\((ii)\) \(\;\) \(a^4+64b^4\)
Solution:
\(\ \ \ \ a^4+64b^4\)
\(=\left( a^{2}\right)^{2} +\left( 8b^{2}\right)^{2}\)
\(=\left( a^{2}\right)^{2} +\left( 8b^{2}\right)^{2} +2\left( a^{2}\right)\left( 8b^{2}\right)\)\(\ -\ \)\(2\left( a^{2}\right)\left( 8b^{2}\right)\)
\(=\left( a^{2} +8b^{2}\right)^{2} -16a^{2} b^{2}\)
\(=\left( a^{2} +8b^{2}\right)^{2} -( 16ab)^{2}\)
\(=\left( a^{2} +8b^{2} +16ab\right)\left( a^{2} +8b^{2} -16ab\right)\)