Question

[thu hương]

 giúp em bài 3 và ý c bài 2 ạ

Answer 1

[Nguyễn Lê Phước Thịnh]

Bài 2:

c: \(C=27x^3-27x^2y+9xy^2-y^3-121\)

\(=\left(3x\right)^3-3\cdot\left(3x\right)^2\cdot y+3\cdot3x\cdot y^2-y^3-121\)

\(=\left(3x-y\right)^3-121=7^3-121=343-121=222\)

Bài 3:

a: \(x^2-4+\left(x-2\right)^2\)

\(=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2\)

=(x-2)(x+2+x-2)

=2x(x-2)

b: \(x^3-2x^2+x-xy^2\)

\(=x\left(x^2-2x+1-y^2\right)\)

\(=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-1-y\right)\left(x-1+y\right)\)

c: \(x^3-4x^2-12x+27\)

\(=\left(x^3+27\right)-4x\left(x+3\right)\)

\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\)

\(=\left(x+3\right)\left(x^2-7x+9\right)\)

d: \(\left(x^2+x\right)^2-2\left(x^2+x\right)-15\)

\(=\left(x^2+x\right)^2-5\left(x^2+x\right)+3\left(x^2+x\right)-15\)

\(=\left(x^2+x\right)\left(x^2+x-5\right)+3\left(x^2+x-5\right)\)

\(=\left(x^2+x-5\right)\left(x^2+x+3\right)\)