Question

[Tạ Thu Hương]

Phân tích đa thức thành nhân tử :
a, 4(2 - x )^2 + xy - 2y
b, 3a^2x - 3a^2y + abx - aby
c, x( x-y)^3 - y(y-x)^2 - y^2(x-y)
d, 2ax^3 + 6ax^2 + 6ax + 18a
e, x^2y - xy^2 - 3x + 3y
f, 3ax^2 + 3bx^2 + bx + 5a + 5b
Giúp mk vs ạ mk đang cần gấp

Answer 1

[Nguyễn Lê Phước Thịnh]

a) Ta có: \(4\left(2-x\right)^2+xy-2y\)

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

\(=\left(x-2\right)\left[4\left(x-2\right)+y\right]\)

\(=\left(x-2\right)\left(4x-8+y\right)\)

b) Ta có: \(3a^2x-3a^2y+abx-aby\)

\(=3a^2\left(x-y\right)+ab\left(x-y\right)\)

\(=\left(x-y\right)\left(3a^2+ab\right)\)

\(=a\left(x-y\right)\left(3a+b\right)\)

c) Ta có: \(x\left(x-y\right)^3-y\left(y-x\right)^2-y^2\left(x-y\right)\)

\(=x\left(x-y\right)^3-y\left(x-y\right)^2-y^2\left(x-y\right)\)

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

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

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

d) Ta có: \(2ax^3+6ax^2+6ax+18a\)

\(=2ax^2\left(x+3\right)+6a\left(x+3\right)\)

\(=\left(x+3\right)\left(2ax^3+6a\right)\)

\(=2a\left(x+3\right)\left(x^3+3\right)\)

e) Ta có: \(x^2y-xy^2-3x+3y\)

\(=xy\left(x-y\right)-3\left(x-y\right)\)

\(=\left(x-y\right)\left(xy-3\right)\)