第1章 1.31

(1)(2)は変換原稿に含まれていません。

(3)

a4+b4+c42a2b22b2c22c2a2=a42a2(b2+c2)+(b42b2c2+c4)a^{4}+b^{4}+c^{4}-2a^{2}b^{2}-2b^{2}c^{2}-2c^{2}a^{2} = a^{4}-2a^{2}(b^{2}+c^{2})+(b^{4}-2b^{2}c^{2}+c^{4})

=a42a2(b2+c2)+(b2c2)2=a42a2(b2+c2)+(b+c)2(bc)2= a^{4}-2a^{2}(b^{2}+c^{2})+(b^{2}-c^{2})^{2} = a^{4}-2a^{2}(b^{2}+c^{2})+(b+c)^{2}(b-c)^{2}

={a+(b+c)}{a(b+c)}{a+(bc)}{a(bc)}= \{a+(b+c)\}\{a-(b+c)\}\{a+(b-c)\}\{a-(b-c)\}

=(a+b+c)(abc)(a+bc)(ab+c)= (a+b+c)(a-b-c)(a+b-c)(a-b+c)

解説: r31bn1z