c: \(=\dfrac{x^3+2x+2x^2+2x+x^2-x+1}{\left(x+1\right)\left(x^2-x+1\right)}\)

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

\(A=4x^2+12xy+9y^2\)

\(B=25x^2-10xy+y^2\)

\(C=8x^3+12x^2y^2+6xy^4+y^6\)

\(D=\left(x^2\right)^2-\left(\dfrac{2}{5}y\right)^2=x^4-\dfrac{4y^2}{25}\)

\(E=x^3-27y^3\)

\(F=x^6-27\)

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

\(=\left(4x^2-9\right)-\left(2x-1\right)^2\)

\(=4x^2-9-\left(4x^2-4x+1\right)\)

\(=4x^2-9-4x^2+4x-1\)

\(=4x-10\)

Lời giải:
a.

$5x-[2x+1-(2x-3)-(4x+1)]=5x-(2x+1-2x+3-4x-1)$

$=5x-(-4x+3)=5x+4x-3=9x-3$

b.

$(-3x^2+2x-1)+(4x^2-2x+3)$

$=-3x^2+2x-1+4x^2-2x+3=x^2+2$

bằng 2^2 =4 

a) (2x+1)^2-2(2x+1)(2x-1)+(2x-1)^2

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

=2^2=4

b)\(\left(2x^3-3x^2+6x-9\right)\left(2x-3\right)\)

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

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

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

tự làm tiếp đi nha

tiếp câu b)

=x(2x-3)(x+1)

a, \(\left(2x+1\right)^2+\left(2x-1\right)^2-2\left(2x+1\right)\left(2x-1\right)\)

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

\(=\left[2x+1-\left(2x-1\right)\right]^2\)

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