Question

(x³-1)(x³+1)(x¹⁸+1)(x³⁵+1)(x⁶+x³+1)(x⁶-x³+1) простите выражение ​

Answer 1

$(x^3-1)(x^3+1)(x^{18}+1)(x^{36}+1)(x^6+x^3+1)(x^6-x^3+1)=\\\\=\Big(\underbrace{(x^3-1)(x^6+x^3+1)}_{(x^3)^3-1^3}\Big)\Big(\underbrace{(x^3+1)(x^6-x^3+1)}_{(x^3)^3+1^3}\Big)(x^{18}+1)(x^{36}+1)=\\\\\\=\Big((x^3)^3-1^3\Big)\Big((x^3)^3+1^3\Big)(x^{18}+1)(x^{36}+1)=\\\\\\=\underbrace{(x^9-1)(x^9+1)}_{(x^9)^2-1^2}(x^{18}+1)(x^{36}+1)=\\\\\\=\underbrace{(x^{18}-1)(x^{18}+1)}_{(x^{18})^2-1^2}(x^{36}+1)=(x^{36}-1)(x^{36}+1)=(x^{36})^2-1^2=\\\\\\=x^{72}-1$

$\boxed {\ a^3-b^3=(a-b)(a^2+ab+b^2)\ \ \ ,\ \ \ a^3+b^3=(a+b)(a^2-ab+b^2)\ }\\\\\\\boxed{\ a^2-b^2=(a-b)(a+b)\ }$