Question

Phân tích đa thức sau thành nhân tử

9y^3-y

8y^3-2y(1-2y)^2

2x^3-8x^2+8x

2x^4-6x^3+6x^2-2x

x^3-6x^2y+9xy^2-x

5x^4-15x^3y+15x^2y^2-5xy^3-5x

3x^2+3xy-x-y

6xy-x^2-y^2+25

7m-7n-m^2+2mn-n^2

3xy-3xz+2xyz-xy^2-xz^2

Answer 1

a)\(9y^3-y\)

\(=y\left(9y^2-1\right)\)

\(=y\left(3y-1\right)\left(3y+1\right)\)

Answer 2

\(9y^3-y=y\left(9y^2-1\right)=y\left(3y+1\right)\left(3y-1\right)\)

\(8y^3-2y\left(1-2y\right)^2=2y\left[\left(2y\right)^2-\left(1-2y\right)^2\right]=2y\left(4y-1\right)\)

\(2x^3-8x^2+8x=2x\left(x^2-4x+4\right)=2x\left(x-2\right)^2\)

Answer 3

\(2x^4-6x^3+6x^2-2x=2x\left(x^3-3x^2+3x-1\right)=2x\left(x-1\right)^3\)\(x^3-8x^2+8x=x\left(x^2-8x+8\right)\)

\(5x^4-15x^3y+15x^2y^2-5xy^3-5x=5x\left(x^3-3x^2y+3xy^2-y^3-1\right)=5x\left[\left(x-y\right)^3-1\right]=5x\left(x-y-1\right)\left(x^2-2xy+y^2+x-y+1\right)\)

Answer 4

\(3x^2+3xy-x-y=x\left(3x-1\right)+y\left(3x-1\right)=\left(3x-1\right)\left(x+y\right)\)

\(7m-7n-m^2+2mn-n^2=7\left(m-n\right)-\left(m-n\right)^2=\left(m-n\right)\left(7-m+n\right)\)\(3xy-3xz+2xyz-xy^2-xz^2=x\left(3y-3z+2yz-y^2-z^2\right)=x\left[3\left(y-z\right)-\left(y-z\right)^2\right]=x\left(y-z\right)\left(3-y+z\right)\)