Question

$(x+1)^{3}$
$(y-2)^{3}$
$( \sqrt{2}-1)^{3}$
$( \sqrt{3}+ \sqrt{2})^{3}$

Answer 1

[tex](a+b)^3=a^3+3a^{2}b+3ab^{2}+b^3\\ (a-b)^3=a^3-3a^{2}b+3ab^{2}-b^3\\\\ a) (x+1)^3=x^3+3 x^{2} +3x+1\\ b) (y-2)^3=y^3-6 y^{2}+12y-8\\ c) ( \sqrt{2}-1 )^3= 2 \sqrt{2}-6+3 \sqrt{2}-1=5 \sqrt{2}-7 \\ d) ( \sqrt{3}+ \sqrt{2})^3=( \sqrt{3} )^3+3* (\sqrt{3})^2* \sqrt{2}+3* \sqrt{3} *( \sqrt{2} )^2+ ( \sqrt{2} )^3=\\ =3 \sqrt{3}+9 \sqrt{2}+6 \sqrt{3}+2 \sqrt{2}=9 \sqrt{3}+11 \sqrt{2} \\[/tex]