Question

Reduzca: (x+5)(x-5)(x4+25x2+625)+56

Answer 1

Respuesta:

$x^{6}-15569$

Explicación paso a paso:

Recuerda :

• $(a+b)(a-b)=a^{2} -b^{2}$
• $(a-b)(a^{2}+ab+b^{2} )=a^{3} -b^{3}$   ;   $(x^{2}-25})(x^{4}+25x^{2} +625)=(x^{2}-25})((x^{2})^{2}+(1)(25)x^{2} +(25)^{2})=(x^{2})^{3}-(25) ^{3}$

Ahora:

$(x+5)(x-5)(x^{4}+25x^{2} +625)+56=(x^{2}-5^{2})(x^{4}+25x^{2} +625)+56=...\\\\...=(x^{2}-25})(x^{4}+25x^{2} +625)+56=(x^{2})^{3} -(25)^{3}=x^{6}-15625+56=...\\\\...=x^{6}-15625+56=x^{6}-15569$