Question

factorize a¹²x⁴-a⁴x¹²

Answer 1

$a^{12} x^{4} - a^{4} x^{12} = a^{4} x^{4} ( a^{8} - x^{8} ) \\ = a^{4} x^{4} [ ( a^{4})^{2} - (x^{4})^{2} \\ =a^{4} x^{4} [( a^{4} + x^{4} )( a^{4} - x^{4} )] \\ = a^{4} x^{4} (a^{4} +x^{4} )( a^{2} - x^{2})( a^{2} +x^{2} ) \\ = a^{4} x^{4} ( a^{4} +x^{4})( a^{2} +x^{2} )(a+x)(a-x)$

Answer 2

$a^{12} x^{4} -a ^{4} x^{12}$
⇒$a^{4} x^{4}(a ^{8}- x^{8} )$
⇒$a^{4} x^{4} [(a^{4})^{2} - (x^{4}) ^{2} ]$
⇒$a^{4} x^{4}(a ^{4}+ x^{4} )(a ^{4} - x^{4} )$
⇒$a^{4} x^{4}(a ^{4}+ x^{4} )[(a ^{2}) ^{2} - (x^{2})^{2} ]$
⇒$a^{4} x^{4}(a ^{4}+ x^{4} )(a ^{2} + x^{2} )( a^{2}- x^{2} )$
⇒$a^{4} x^{4}(a ^{4}+ x^{4} )(a ^{2} + x^{2} )( a^{2}- x^{2} )$
⇒$a^{4} x^{4}(a ^{4}+ x^{4} )(a ^{2} + x^{2} )( a- x )(a+x)$
Ans:$a^{4} x^{4}(a ^{4}+ x^{4} )(a ^{2} + x^{2} )( a- x )(a+x)$