Bài 4A.
a.
\(A=(2x-1)^3-6x.(2x-1)^2+12x^2(2x-1)-8x^3\)
\(=(2x-1)^3-3.2x.(2x-1)^2+3(2x)^2(2x-1)-(2x)^3\)
\(=[(2x-1)-(2x)]^3=(-1)^3=-1\)
b.
\(B=(x^2-2xy)^3+3(x^2-2xy)^2y^2+3(x^2-2xy)y^4+y^6\)
\(=[(x^2-2xy)+y^2]^3=[(x-y)^2]^3=(x-y)^6\)
Bài 4B:
a: Ta có: \(C=\left(x-1\right)^3+3x\left(x-1\right)^2+3x^2\left(x-1\right)+x^3\)
\(=\left(x-1+x\right)^3\)
\(=\left(2x-1\right)^3\)
\(=8x^3-12x+6x-1\)
b: Ta có: \(D=\left(y^2-x\right)^3-3\left(x-y^2\right)^2\cdot y^2+3\left(y^2-x\right)y^4-y^6\)
\(=\left(y^2-x-y^2\right)^3\)
\(=\left(-x\right)^3=-x^3\)
Bài 4B.
a.
\(C=(x-1)^3+3x(x-1)^2+3x^2(x-1)+x^3=[(x-1)+x]^3\)
\(=(2x-1)^3\)
b.
\(D=(y^2-x)^3-3(x-y^2)^2y^2+3(y^2-x)y^4-y^6\)
\(=(y^2-x)^3-3(y^2-x)^2y^2+3(y^2-x)(y^2)^2-(y^2)^3\)
\(=[(y^2-x)-y^2]^3=(-x)^3=-x^3\)
Bài 4A:
a: Ta có: \(A=\left(2x-1\right)^3-6x\left(2x-1\right)^2+12x^2\left(2x-1\right)-8x^3\)
\(=\left(2x-1-2x\right)^3\)
=-1
b: Ta có: \(B=\left(x^2-2xy\right)^3+3\left(x^2-2xy\right)^2y^2+3\left(x^2-2xy\right)y^4+y^6\)
\(=\left(x^2-2xy+y^2\right)^3\)
\(=\left(x-y\right)^6\)
