Question

Phân tích đa thức thành nhân tử:
a) x^2y + 2xy^2 + xy

b) x^3 + x^2 – 4x – 4

c) x^2 – 2x – 15

d) x^2 – 4 + (x – 2)^2

e) x^2 – y^2 + 2x + 1

g) (x + 9)^2 – 36x^2
h) x^2 – 2xy + y^2 – z^2 + 2zt – t^2

i) x^3 – 3x^2 + 3x – 1 – y^3

Answer 1

\(a,=xy\left(x+2y+1\right)\\ b,=x^2\left(x+1\right)-4\left(x+1\right)=\left(x+1\right)\left(x-2\right)\left(x+2\right)\\ c,=x^2-5x+3x-15=\left(x-5\right)\left(x+3\right)\\ d,=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2=\left(x-2\right)\left(x+2+x-2\right)=2x\left(x-2\right)\\ e,=\left(x+1\right)^2-y^2=\left(x+y+1\right)\left(x-y+1\right)\\ g,=\left(x+9-6x\right)\left(x+9+6x\right)=\left(9-5x\right)\left(7x+9\right)\\ h,=\left(x-y\right)^2-\left(z-t\right)^2=\left(x-y-z+t\right)\left(x-y+z-t\right)\\ i,=\left(x-1\right)^3-y^3=\left(x-y-1\right)\left(x^2-2x+1+xy+y+y^2\right)\)

Answer 2

c: =(x-5)(x+3)

e: =(x+1-y)(x+1+y)