(2x + y)(4x2 – 2xy + y2) – (2x – y)(4x2 + 2xy + y2)

= (2x + y)[(2x)2 – 2x.y + y2] – (2x – y)[(2x)2 + 2x.y + y2]

= [(2x)3 + y3] – [(2x)3 – y3]

= (2x)3 + y3 – (2x)3 + y3

= 2y3

a,sửa đề :  \(\left(\frac{1}{x^2+4x+4}-\frac{1}{x^2-4x+4}\right):\left(\frac{1}{x+2}+\frac{1}{x^2-4}\right)\)

\(=\left(\frac{1}{\left(x+2\right)^2}-\frac{1}{\left(x-2\right)^2}\right):\left(\frac{x-2+1}{\left(x+2\right)\left(x-2\right)}\right)\)

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

\(=\frac{-8x\left(x+2\right)\left(x-2\right)}{\left(x+2\right)^2\left(x-2\right)^2\left(x-1\right)}=\frac{-8x}{\left(x-1\right)\left(x^2-4\right)}\)

b, \(\left(\frac{2x}{2x-y}-\frac{4x^2}{4x^2+4xy+y^2}\right):\left(\frac{2x}{4x^2-y^2}+\frac{1}{y-2x}\right)\)

\(=\left(\frac{2x}{2x-y}-\frac{4x^2}{\left(2x+y\right)^2}\right):\left(\frac{2x}{\left(2x-y\right)\left(2x+y\right)}-\frac{1}{2x-y}\right)\)

\(=\left(\frac{2x\left(2x+y\right)^2-4x^2\left(2x-y\right)}{\left(2x-y\right)\left(2x+y\right)^2}\right):\left(\frac{2x-\left(2x+y\right)}{\left(2x-y\right)\left(2x+y\right)}\right)\)

\(=\left(\frac{8x^3+8x^2y+2xy^2-8x^3+4x^2y}{\left(2x-y\right)\left(2x+y\right)^2}\right):\left(\frac{-y}{\left(2x-y\right)\left(2x+y\right)}\right)\)

\(=-\left(\frac{12x^2y+xy^2}{2x+y}\right)=\frac{-12x^2y-xy^2}{2x+y}\)

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

\(=4x^4-4x^2\)

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

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

c. \(\left(2x+1\right)\left(2x-1\right)-4x^2=\left(2x\right)^2-1^2-4x^2=4x^2-1-4x^2=-1\)

d. \(\left(2x^{3y}+y\right)^2-\left(y-2x^{3y}\right)^2\)

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

\(=2y.2.2x^{3y}=4y.2x^{3y}\)

a/ \(\left(2x+1\right)\left(2x-1\right)-4x^2=\left(2x\right)^2-1^2-4x^2\)

\(=4x^2-1-4x^2\)

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

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

c/ \(\left(2x^2+y\right)^2-\left(2x^2-y\right)^2\)

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

\(=4x^2\cdot2y=8x^2y\)

d/ \(\left(2x^3y+y\right)^2-\left(y-2x^3y\right)^2=\left(2x^3y+y\right)^2-\left(2x^3y-y\right)^2\)

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

\(=4x^3y\cdot2y=8x^3y^2\)

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

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

\(=[\left(2x\right)^3-y^3]-[\left(2x\right)^3+y^3]\)

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

\(=-2y^3\)

(4x²+2xy+y²)(2x-y)-(2x-y)(4x²-2xy+y²)

=(2x³-y³)-(2x+y)(4x²-2xy+y²)

=(2x³-y³)-(2x³+y³)

=2x³-y³-2x³+y³

=0

( 2x + y ) ( 4x² - 2xy + y² ) - ( 2x - y ) ( 4x² + 2xy + y² )

= 8x³ + y³ - ( 8x³ - y³ )
= 2y³ 

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

\(=8x^3+y^3-\left(8x^3-y^3\right)\)

\(=8x^3+y^3-8x^3+y^3\)

\(=\left(8x^3-8x^3\right)+\left(y^3+y^3\right)\)

\(=2y^3\)

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

\(4x^2+4xy+y^2\)