Question

Пжжжжжж!!! 20балов!!!​

Answer 1

$a^3+b^3=(a+b)(a^2-ab+b^2)$

$4)\ \ \Big(x^{1/6}+2\Big)\Big(x^{1/3}-2x^{1/6}+4\Big)=\Big(x^{1/6}\Big)^3+2^3=x^{1/2}+8=\sqrt x+8$

$(a-b)^2=a^2-2ab+b^2$

$5)\ \ \Big(y^{1.5}-4y^{0.5}\Big)^2+8y^2=\Big(y^{3/2}\Big)^2-2\cdot y^{3/2}\cdot 4y^{1/2}+\Big(4y^{1/2}\Big)^2+8y^2=\\\\=y^3-8y^{4/2}+16y+8y^2=y^3+16y-8y^2+8y^2=y^3+16y$

$(a-b)(a+b)=a^2-b^2$

$6)\ \ \Big(a^{1/8}-1\Big)\Big(a^{1/4}+1\Big)\Big(a^{1/8}+1\Big)=\bigg(\Big(a^{1/8}\Big)^2-1^2\bigg)\bigg(a^{1/4}+1\bigg)=\\\\=\Big(a^{1/4}-1\Big)\Big(a^{1/4}+1\Big)=\Big(a^{1/4}\Big)^2-1^2=a^{1/2}-1=\sqrt a -1$