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Factorize the following expressions:

a^{12} + b^{12}

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#### Solution

= (a^{4})^{3} + (b^{4})^{3}

= (a^{4})^{3} + (b^{4} )^{3}

= (a^{4} + b^{4} )((a^{4})^{2} - a^{4} x b^{4} + (b^{4} )^{2}) [∵ a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2} )]

= (a^{4} + b^{4} )(a^{8} - a^{4}b^{4} + b^{8} )

∴ a^{12} + b^{12} = (a^{4} + b^{4})(a^{8} - a^{4}b^{4} + b^{8})

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