1. 

2.

 \(\begin{array}{l}\left( {3x - 2y} \right)\left( {9{x^2} + 6xy + 4{y^2}} \right) + 8{y^3}\\ = \left( {3x - 2y} \right)\left[ {{{\left( {3x} \right)}^2} + 3x.2y + {{\left( {2y} \right)}^2}} \right] + 8{y^3}\\ = {\left( {3x} \right)^3} - {\left( {2y} \right)^3} + 8{y^3}\\ = 27{x^3} - 8{y^3} + 8{y^3}\\ = 27{x^3}\end{array}\)

1)  2xy²+x²y⁴+1=(xy²)²+2xy².1+1²=(xy²+1)²

2)

a)2(x-y)(x+y)+(x+y)²+(x-y)²=(x+y+x-y)²=(2x)²=4x²

b)(x-y+z)²+(z-y)²+2(x-y+z)(y-z)

=(x-y+z)²+(y-z)²+2(x-y+z)(y-z)

=(x-y+z+y-z)²

=x²

Check lại :v

\(\begin{array}{l}\left( {x - 2y} \right)\left( {{x^2} + 2xy + 4{y^2}} \right) + \left( {x + 2y} \right)\left( {{x^2} - 2xy + 4{y^2}} \right)\\ = {x^3} - {\left( {2y} \right)^3} + {x^3} + {\left( {2y} \right)^3}\\ = {x^3} - 8{y^3} + {x^3} + 8{y^3}\\ = 2{x^3}\end{array}\)

1.\(=x^3+8y^3-x^3+8y^3+2y^3=18y^3\)

2. \(=x^3-3x^2+3x-1+1-x^3+3\left(9-x^2\right)\)

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

Ko chắc lém :))))

f: \(x^2y^2+2xy+1=\left(xy+1\right)^2\)

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

h: \(\left(x-3y\right)^2-8\left(x-3y\right)+16=\left(x-3y-4\right)^2\)

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

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

a)      \({x^3} + 512 = \left( {x + 8} \right)\left( {{x^2} - 8x + 64)} \right)\)

b)      \(27{x^3} - 8{y^3} = \left( {3x - 2y} \right)\left( {9{x^2} + 6xy + 4{y^2}} \right)\)

a)

\(\begin{array}{l}\left( {2x - 5y} \right)\left( {2x + 5y} \right) + {\left( {2x + 5y} \right)^2}\\ = \left( {2x + 5y} \right)\left( {2x - 5y + 2x + 5y} \right)\\ = \left( {2x + 5y} \right).4x\\ = 2x.4x + 5y.4x\\ = 8{x^2} + 20xy\end{array}\)

b)

\(\begin{array}{l}\left( {x + 2y} \right)\left( {{x^2} - 2xy + 4{y^2}} \right) + \left( {2x - y} \right)\left( {4{x^2} + 2xy + {y^2}} \right)\\ = {x^3} + {\left( {2y} \right)^3} + {\left( {2x} \right)^3} - {y^3}\\ = {x^3} + 8{y^3} + 8{x^3} - {y^3}\\ = \left( {{x^3} + 8{x^3}} \right) + \left( {8{y^3} - {y^3}} \right)\\ = 9{x^3} + 7{y^3}\end{array}\)