a: \(\left(a+b\right)^3-\left(a-b\right)^3\)

\(=a^3+3a^2b+3ab^2+b^3-a^3+3a^2b-3a^2b+b^3\)

\(=6a^2b+2b^3\)

\(=2b\left(3a^2+b^2\right)\)

\(a,=\left(3x+\dfrac{y}{2}\right)\left(9x^2+\dfrac{3}{2}xy+\dfrac{y^2}{4}\right)\\ b,=\left(5x+3y\right)\left(25x^2+15xy+9y^2\right)\)

\(a,=\left(5x-1\right)^2\\ b,=\left(x+4\right)^2\\ c,=\left(4x+3y\right)^2\\ d,=\left(\dfrac{x}{4}+2y\right)^2\)

\(a,=\left(3x-11\right)\left(3x+11\right)\\ b,=\left(3x+1-x+2\right)\left(3x+1+x-2\right)\\ =\left(2x+3\right)\left(4x-1\right)\\ c,=\left(2x+1-8\right)\left(2x+1+8\right)=\left(2x-7\right)\left(2x+9\right)\)

\(a,=\left(3x+2y\right)^3\\ b,=\left(4-x\right)^3\\ c,=\left(\dfrac{1}{2}x-3y\right)^3\)

a)
\(=x^3+3.x^2.1+3.x.1^2+1^3\)
\(=x^3+3x^2+3x+1\)
b)
\(=\left(2x\right)^3+3.\left(2x\right)^2.3+3.2x.3^2+3^3\)
\(=8x^3+36x^2+54x+27\)
c)
\(x^3+3.x^2.\dfrac{1}{2}+3.x.\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3\)
\(=x^3+1,5x^2+0,75x+0,125\)

d)
=\(\left(x^2\right)^3-3.\left(x^2\right)^2.2+3.x^2.2^2-2^3\)
\(=x^5-6x^4+12x^2-8\)
e)
\(=\left(2x\right)^3-3.\left(2x\right)^2.3y+3.2x.\left(3y\right)^2-\left(3y\right)^3\)
\(=8x^3-36x^2y+54xy^2-27y^3\)

\(A=\left(X+3\right)^3\)

Thay x = - 3 vào, ta có:

\(A=\left(-3+3\right)^3=0\)

\(D=x^3-3x^2y+3xy^2-y^3-3x^3+6x^2y-3xy^2+3x^3-3x^2y-x^3\\ D=-y^3\)

a: \(\left(3x-2\right)^2=9x^2-12x+4\)

c: \(9x^2-225=9\left(x^2-25\right)=9\left(x-5\right)\left(x+5\right)\)