Respuestas

2013-10-11T23:43:37+02:00
Factorizacion aplicando Productos Notables  

M(a,b)=64 a^{7}b^{7}-ab^{13}=ab^{7}[64a^{6}-b^{6}]= ab^{7}[8^{2}(a^{3})^{2}-(6^{3})^{2}]

       =ab^{7}[(8a^{3})^{2}-(b^{3})^{2}]=ab^{7}[(8a^{3}+b^{3})(8a^{3}-b^{3})]

       =ab^{7}[(2^{3}a^{3}+b^{3})(2^{3}a^{3}-b^{3})]

        =ab^{7}[((2a)^{3}+b^{3})((2a)^{3}-b^{3})]

         =ab^{7}[(2a+b)(4a^{2}-2ab+b^{3})][(2a-b)(4a^{2}+2ab+b^{3})]

Luego: M(a,b)=ab^{7}(2a+b)(4a^{2}-2ab+b^{3})(2a-b^{2})(4a^{2}+2ab+b^{3})

Por tanto M(a,b) Tiene 6 FACTORES PRIMOS.