Bài phân tích đa thức thành nhân tử:
a) 3x\(^2\) - 8xy + 5y\(^2\)
b) 8xy\(^3\) + x.(x - y)\(^3\)
c) 2x( x-3) - x + 3
d) x\(^4\) - 4x\(^3\) + 4x\(^2\)
e) 4x\(^2\) + 4xy - 4z\(^2\) + y\(^2\) - 4z - 1
f) x\(^2\) - 2xy + y\(^2\) - x + y - 6
g) x\(^2\) ( x + 3)\(^2\) - ( x+3 ) \(^2\) - ( x\(^2\) - 1)
Mong m.n giúp ạ!!
Phân tích đa thức thành nhân tử:
a) Ta có: \(3x^2-8xy+5y^2\)
\(=3x^2-3xy-5xy+5y^2\)
\(=3x\left(x-y\right)-5y\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5y\right)\)
b) Ta có: \(8xy^3+x\left(x-y\right)^3\)
\(=x\left[8y^3-\left(x-y\right)^3\right]\)
\(=x\left[2y-\left(x-y\right)\right]\left[4y^2+2y\left(x-y\right)+\left(x-y\right)^2\right]\)
\(=x\left(2y-x+y\right)\left(4y^2+2xy-2y^2+x^2-2xy+y^2\right)\)
\(=x\left(3y-x\right)\left(3y^2+x^2\right)\)
c) Ta có: \(2x\left(x-3\right)-x+3\)
\(=2x\left(x-3\right)-\left(x-3\right)\)
\(=\left(x-3\right)\left(2x-1\right)\)
d) Ta có: \(x^4-4x^3+4x^2\)
\(=x^2\left(x^2-4x+4\right)\)
\(=x^2\cdot\left(x-2\right)^2\)
e) Ta có: \(4x^2+4xy-4z^2+y^2-4z-1\)
\(=\left(4x^2+4xy+y^2\right)-\left(4z^2+4z+1\right)\)
\(=\left(2x+y\right)^2-\left(2z+1\right)^2\)
\(=\left(2x+y-2z-1\right)\left(2x+y+2z+1\right)\)
f) Ta có: \(x^2-2xy+y^2-x+y-6\)
\(=\left(x-y\right)^2-\left(x-y\right)-6\)
\(=\left(x-y\right)^2-3\left(x-y\right)+2\left(x-y\right)-6\)
\(=\left(x-y\right)\left(x-y-3\right)+2\left(x-y-3\right)\)
\(=\left(x-y-3\right)\left(x-y+2\right)\)
g) Ta có: \(x^2\left(x+3\right)^2-\left(x+3\right)^2-\left(x^2-1\right)\)
\(=x^2\left(x^2+6x+9\right)-\left(x^2+6x+9\right)-x^2+1\)
\(=\left(x^2-6x+9\right)\left(x^2-1\right)-\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2-6x+9-1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2-6x+8\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x-4\right)\)
