Bài 3A:
a: Ta có: \(A=\left(1-2x\right)\left(4x^2+2x+1\right)+8\left(x-1\right)\left(x^2+x+1\right)\)
\(=1-8x^3+8\left(x^3-1\right)\)
\(=1-8x^3+8x^3-8\)
=-7
b: Ta có: \(B=\left(x^2-2y\right)\left(x^4+2x^2y+4y^2\right)-x^3\left(x-y\right)\left(x^2+xy+y^2\right)+8y^3\)
\(=x^6-8y^3-x^3\left(x^3-y^3\right)+8y^3\)
\(=x^6-x^6+x^3y^3\)
\(=x^3y^3\)
Bài 2B:
a: \(M=\left(x+2\right)\left(x^2-2x+4\right)=x^3+8\)
b: \(N=\left(1-\dfrac{x}{5}\right)\left(\dfrac{x^2}{25}+\dfrac{x}{5}+1\right)=1-\dfrac{x^3}{125}\)
c: \(P=\left(3x-y\right)\left(9x^2+3xy+y^2\right)=27x^3-y^3\)
d: \(Q=\left(4y-\dfrac{x}{2}\right)\left(\dfrac{x^2}{4}+2xy+16y^2\right)=64y^3-\dfrac{x^3}{8}\)
3B:
a: Ta có: \(A=\left(4-x\right)\left(x^2+4x+16\right)+\left(x-1\right)\left(x^2+x+1\right)\)
\(=64-x^3+x^3-1\)
=63
b: Ta có: \(B=3\left(x-\dfrac{1}{3}y\right)\left(9x^2+3xy+y^2\right)+\left(x+y\right)\left(x^2-xy+y^2\right)-27x^3\)
\(=\left(3x-y\right)\left(9x^2+3xy+y^2\right)+\left(x+y\right)\left(x^2-xy+y^2\right)-27x^3\)
\(=27x^3-y^3+x^3+y^3-27y^3\)
\(=x^3\)
