a: \(\left(x+7\right)^3=x^3+21x^2+147x+343\)
b: \(\left(5-x\right)^3=125-75x+15x^2-x^3\)
c: \(\left(5x-1\right)^3=125x^3-75x^2+15x-1\)
d: \(\left(2x+3y\right)^3=8x^3+36x^2y+54xy^2+27y^3\)
e: \(\left(\dfrac{1}{2}x-3\right)^3=\dfrac{1}{8}x^3-\dfrac{9}{4}x^2+\dfrac{27}{2}x-27\)
f: \(\left(x-1\right)^3-x\cdot\left(x-3\right)^2+1\)
\(=x^3-3x^2+3x-1-x^3+6x^2-9x+1\)
\(=3x^2-6x\)
g: \(\left(x+2\right)^3-x^2\cdot\left(x+6\right)\)
\(=x^3+6x^2+12x+8-x^3-6x^2\)
=12x+8
h: Ta có: \(\left(a+b\right)^3-\left(a-b\right)^3-2b^3\)
\(=a^3+3a^2b+3ab^2+b^3-a^3+3a^2b-3ab^2+b^3-2b^3\)
\(=6a^2b\)
i: Ta có: \(\left(a+2b\right)^3-6ab\left(a+2b\right)\)
\(=a^3+6a^2b+12ab^2+8b^3-6a^2b-12ab^2\)
\(=a^3+8b^3\)
j: \(\left(x+3\right)^3=x^3+9x^2+27x+27\)
ka: Ta có: \(\left(a+1\right)^3+\left(a-1\right)^3+a^3-3a\left(a+1\right)\left(a-1\right)\)
\(=a^3+3a^2+3a+1+a^3-3a^2+3a-1+a^3-3a\left(a^2-1\right)\)
\(=3a^3+6a-3a^3+3a\)
=9a
