1: \(\left(x+1\right)^3=x^3+3x^2+3x+1\)

2: \(\left(x-1\right)^3=x^3-3x^2+3x-1\)

3: \(x^3+1=\left(x+1\right)\left(x^2-x+1\right)\)

4: \(x^3-1=\left(x-1\right)\left(x^2+x+1\right)\)

5: \(\left(x+2\right)^3=x^3+6x^2+12x+8\)

\(\sqrt{21-12\sqrt{3}}=\sqrt{21-2.\sqrt{36}.\sqrt{3}}=\sqrt{21-2\sqrt{108}}=\sqrt{12-2.\sqrt{12}.\sqrt{9}+9}=\sqrt{\left(\sqrt{12}-3\right)^2}=\sqrt{12}-3\)

\(\sqrt{21-12\sqrt{3}}=2\sqrt{3}-3\)

`1)(a^[1/4]-b^[1/4])(a^[1/4]+b^[1/4])(a^[1/2]+b^[1/2])`

`=[(a^[1/4])^2-(b^[1/4])^2](a^[1/2]+b^[1/2])`

`=(a^[1/2]-b^[1/2])(a^[1/2]+b^[1/2])`

`=a-b`

`2)(a^[1/3]-b^[2/3])(a^[2/3]+a^[1/3]b^[2/3]+b^[4/3])`

`=(a^[1/3]-b^[2/3])[(a^[1/3])^2+a^[1/3]b^[2/3]+(b^[2/3])^2]`

`=(a^[1/3])^3-(b^[2/3])^3`

`=a-b^2`

10+2 căn 5

= 10+2 căn 10 . căn 2 trên 2+2 trên 4

= (căn 10+ căn 2 trên 2) ²

mik ko biết viết căn nhé, bạn tự dịch, còn kqua sai thì thôi nhé

\(=\sqrt{3-2\sqrt{3}+1}=\sqrt{\left(\sqrt{3}-1\right)^2}=\left|\sqrt{3}-1\right|=\sqrt{3}-1\)

\(\dfrac{x^3-27}{x^2-9}\left(x\ne\pm3\right)\)

\(=\dfrac{x^3-3^3}{x^2-3^2}\)

\(=\dfrac{\left(x-3\right)\left(x^2+3x+9\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{x^2+3x+9}{x+3}\)

ĐKXĐ: a>=6

\(\dfrac{a-7}{\sqrt{a-6}+1}=\sqrt{a-6}-1\)

\(A=\dfrac{\left|a-5\right|}{5-a}+\sqrt{a-6}\)

\(=\dfrac{a-5}{5-a}+\sqrt{a-6}=\sqrt{a-6}-1\)(ĐPCM)

\(\sqrt{7+4\sqrt{3}}=\sqrt{\left(2+\sqrt{3}\right)^2}=2+\sqrt{3}\)

\(\sqrt{8-2\sqrt{12}}=\sqrt{\left(\sqrt{6}-\sqrt{2}\right)^2}=\left|\sqrt{6}-\sqrt{2}\right|=\sqrt{6}-\sqrt{2}\)

\(\sqrt{21+6\sqrt{6}}=\sqrt{\left(3\sqrt{2}-\sqrt{3}\right)^2}=\left|3\sqrt{2}-\sqrt{3}\right|=3\sqrt{2}-\sqrt{3}\)

\(\sqrt{15-6\sqrt{6}}=\sqrt{\left(3-\sqrt{6}\right)^2}=\left|3-\sqrt{6}\right|=3-\sqrt{6}\)

\(\sqrt{29-12\sqrt{5}}=\sqrt{\left(2\sqrt{5}-3\right)^2}=\left|2\sqrt{5}-3\right|=2\sqrt{5}-3\)

\(\sqrt{41+12\sqrt{5}}=\sqrt{\left(6+\sqrt{5}\right)^2}=6+\sqrt{5}\)

\(=2\left(m^2-10m+7\right)=2\left(m^2-10m+25-18\right)\)

\(=2\left(m^2-10m+25\right)-36=2\left(m-5\right)^2-36\ge-36\)  \(\forall m\)