d: \(=-\left(x+\sqrt{x}-12\right)=-\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)\)

a, \(\dfrac{x^2}{4}-xy+y^2=\left(\dfrac{x}{2}\right)^2-xy+y^2=\left(\dfrac{x}{2}\right)^2-2.\dfrac{x}{2}.y+y^2\)

\(=\left(\dfrac{x^2}{2}-y\right)^2\)

b, \(x^2+x+\dfrac{1}{4}=x^2+\dfrac{1}{2}.2.x+\left(\dfrac{1}{2}\right)^2=\left(x+\dfrac{1}{2}\right)^2\)

c, \(x^2+2\sqrt{3}x+3=x^2+2\sqrt{3}x+\left(\sqrt{3}\right)^2=\left(x+\sqrt{3}\right)^2\)

d, \(4x^2-1=\left(2x-1\right)\left(2x+1\right)\)

`x^2/4-2*x/2*y+y^2`

`=(x/2-y)^2`

`x^2+x+1/4`

`=x^2+2*x*1/2+(1/2)^2`

`=(x+1/2)^2`

`x^2+2sqrt3x+3`

`=x+2xsqrt3+sqrt3^2`

`=(x+sqrt3)^2`

`4x^2-1`

`=(2x)^2-1`

`=(2x-1)(2x+1)`

\(M=7\sqrt{x-1}-\sqrt{x^2\left(x-1\right)}+\left(\sqrt{x-1}\right)^2=\sqrt{x-1}\left(7-x+\sqrt{x-1}\right)\)

\(=\sqrt{x-1}\left(6-\left(x-1\right)+\sqrt{x-1}\right)\)( đến đây bạn có thể đặt \(\sqrt{x-1}=t\),t>=0 rồi giải)

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

Câu b đề sai nha bạn.

a) \(x^3+9x^2+27x+27=\left(x+3\right)^3\)

b) \(3\sqrt{3x^3}+18x^2+12\sqrt{3x}+8=\left(\sqrt{3x}+2\right)^3\)

c) \(\dfrac{1}{4}-x^2=\left(\dfrac{1}{2}-x\right)\left(\dfrac{1}{2}+x\right)\)

1: \(x-9=\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)\)

2: \(x-16=\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)\)

3: \(9x-1=\left(3\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)\)

4: \(x\sqrt{x}+1=\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)\)

\(1,x-9=\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)\\ 2,x-16=\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)\\ 3,9x-1=\left(3\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)\\ 4,x\sqrt{x}+1=\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)\)

 1,x−9=(√x−3)(√x+3)

2,x−16=(√x−4)(√x+4)

3,9x−1=(3√x−1)(3√x+1)

4,x√x+1=(√x+1)(x−√x+1

\(2+\sqrt{3}+\sqrt{6}+\sqrt{8}=2+\sqrt{3}+\sqrt{6}+2\sqrt{2}\)

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

\(2+\sqrt{3}+\sqrt{6}+\sqrt{8}=\left(\sqrt{2}+1\right)\left(2+\sqrt{3}\right)\)