câu b sai r 

\(\dfrac{1}{3}xy+x^2z+xz=3x\left(\dfrac{1}{9}y+\dfrac{1}{3}xz+\dfrac{1}{3}z\right)\)

Lời giải:

a.

$=\frac{1}{2}(x^2-4y^2)=\frac{1}{2}[x^2-(2y)^2]=\frac{1}{2}(x-2y)(x+2y)$

b.

$=\frac{1}{3}x(y+3xz+3z)$

c.

$=\frac{2}{25}x(225x^2-4)=\frac{2}{25}(15x-2)(15x+2)$

d.

$=\frac{1}{5}x^2(2+25x+5y)$

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

B

a: \(\frac12x^2-2y^2=\frac12\left(x^2-4y^2\right)\)

\(=\frac12\left(x-2y\right)\left(x+2y\right)\)

b: \(\frac13xy+x^2z+xz\)

\(=x\cdot\frac13y+x\cdot xz+x\cdot z\)

\(=x\left(\frac13y+xz+z\right)\)

c: \(18x^3-\frac{8}{25}x=2x\left(9x^2-\frac{4}{25}\right)\)

\(=2x\left\lbrack\left(3x\right)^2-\left(\frac25\right)^2\right\rbrack\)

\(=2x\left(3x-\frac25\right)\left(3x+\frac25\right)\)

d: \(\frac25x^2+5x^3+x^2y=x^2\cdot\frac25+x^2\cdot5x+x^2\cdot y=x^2\left(\frac25+5x+y\right)\)

e: \(\frac12\left(x^2+y^2\right)^2-2x^2y^2\)

\(=\frac12\left\lbrack\left(x^2+y^2\right)^2-4x^2y^2\right\rbrack\)

\(=\frac12\left(x^2+y^2-2xy\right)\left(x^2+y^2+2xy\right)\)

\(=\frac12\left(x-y\right)^2\cdot\left(x+y\right)^2\)

f: \(27x^3-\frac18y^3=\left(3x\right)^3-\left(\frac12y\right)^3\)

\(=\left(3x-\frac12y\right)\left(9x^2+\frac32xy+\frac14y^2\right)\)

\(=\left(x^2+2x\right)^2+9\left(x^2+2x\right)+20\)

\(=\left(x^2+2x+4\right)\left(x^2+2x+5\right)\)

=5(x²-\(\frac{18}{5}x\)-\(\frac{8}{5}\))=5(x²+\(\frac{2}{5}x-4x-\frac{8}{5}\))

=5(x-4)(\(\frac{2}{5}+x\))

5x²-18x-8

=5x²+2x-20x-8

=x(5x+2)-4(5x+2)

=(x-4)(5x+2)

\(-8x^3+1=1^3-\left(2x\right)^3=\left(1-2x\right)\left(1+2x+4x^2\right)\)

\(4\left(x^2+15x+50\right)\left(x^2+18x+72\right)-3x^2\)

\(=4\left(x+5\right)\left(x+10\right)\left(x+12\right)\left(x+6\right)-3x^2\)

\(=4\left(x^2+17x+60\right)\left(x^2+16x+60\right)-3x^2\)

\(=4\left(x+60\right)^2+132x\left(x+60\right)+1088x^2-3x^2\)

\(=4\left(x+60\right)^2+132x\left(x+60\right)+1085x^2\)

\(=4\left(x+60\right)^2+62x\left(x+60\right)+70x\left(x+60\right)+1085x^2\)

\(=2\left(x+60\right)\left[2\left(x+60\right)+31x\right]+35x\left[2\left(x+60\right)+31x\right]\)

\(=\left(33x+120\right)\left(2x+120+35x\right)\)

\(=3\left(11x+40\right)\left(37x+120\right)\)

\(\Rightarrow\left(x^2+2x\right)^2+9\left(x^2+2x\right)+20=\left(x^2+2x\right)^2+4\left(x^2+2x\right)+5\cdot\left(x^2+2x\right)+20=\left(x^2+2x\right)\left(x^2+2x+4\right)+5\left(x^2+2x+4\right)=\left(x^2+2x+4\right)\left(x^2+2x+5\right)\)