Question

Find the product using the formula: (a2 + b2) (a2 - b2) (a4 + b4) (a 8 + b 8)​

Answer 1

Step-by-step explanation:

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Answer 2

$(a {}^{2} + b {}^{2} )(a {}^{2} - b {}^{2} )(a {}^{4} + b {}^{4})( a {}^{8} + b {}^{8}) \\ = ((a {}^{2} ) {}^{2} - (b {}^{2} ) {}^{2} )(a {}^{4} + b {}^{4} )(a {}^{8} + b {}^{8} ) \\ = (a {}^{4} - b {}^{4})( a {}^{4} + b {}^{4} )( {}a^{8} + b {}^{8} ) \\ = ((a {}^{4}) {}^{2} - (b {}^{4}) {}^{2} )( a {}^{8} + b {}^{8} ) \\ = (a {}^{8} - b {}^{8} )(a {}^{8} + b {}^{8} ) \\ = ((a {}^{8} ) {}^{2} - ( b {}^{8}) {}^{2} ) \\ = (a {}^{16} - b {}^{16 } )$

The above problem is solved by the formula

$(a + b)(a - b) = (a {}^{2} - b {}^{2} )$