Bài 6:
a: Ta có: \(Q=\left(3x-1\right)\left(9x^2-3x+1\right)-\left(1-3x\right)\left(1+3x+9x^2\right)\)
\(=27x^3-1-\left(1-27x^3\right)\)
\(=27x^3-1-1+27x^3\)
\(=54x^3-2\)
\(=54000-2=53998\)
b: Ta có: \(P=\left(\dfrac{x}{4}\right)^3+\left(\dfrac{y}{2}\right)^3\)
\(=\left(\dfrac{1}{4}x+\dfrac{1}{2}y\right)^3-3\cdot\dfrac{1}{4}x\cdot\dfrac{1}{2}y\cdot\left(\dfrac{1}{4}x+\dfrac{1}{2}y\right)\)
\(=\dfrac{\left(x+2y\right)^3}{64}-3\cdot\dfrac{1}{8}\cdot\left(-6\right)\cdot0\)
\(=0\)
Bài 7:
a: \(\left(x+\dfrac{1}{2}\right)\left(x^2-\dfrac{1}{2}x+\dfrac{1}{4}\right)=x^3+\dfrac{1}{8}\)
b: \(\left(x-3y\right)\left(x^2+3xy+9y^2\right)=x^3-27y^3\)
c: \(\left(x^2-3\right)\left(x^4+3x^2+9\right)=x^6-27\)
d: \(\left(2x-1\right)\left(4x^2+2x+1\right)=8x^3-1\)
Bài 6A:
a: Ta có: \(M=\left(6x+2\right)\left(9x^2-3x+1\right)-\left(x+1\right)\left(x^2-x+1\right)\)
\(=2\left(3x+1\right)\left(9x^2-3x+1\right)-\left(x^3+1\right)\)
\(=2\left(27x^3+1\right)-x^3-1\)
\(=54x^3+2-x^3-1\)
\(=53x^3+1\)
\(=\dfrac{53}{8}+1=\dfrac{61}{8}\)
b: Ta có: \(N=x^3+y^3+6x^2y^2\left(x+y\right)+3xy\left(x^2+y^2\right)\)
\(=\left(x+y\right)^3-3xy\left(x+y\right)+6x^2y^2+3xy\cdot\left(-2xy\right)\)
\(=1-3xy+6x^2y^2+6x^2y^2\)
\(=12x^2y^2-3xy+1\)
