Question

phân tích đa thức thành nhân tử

a) x^3 +x^2y -xy^2 -y^3

b) x^2y^2 +1 -x^2 -y^2

c) x^2 -y^2 -4x +4y

d) x^2 -y^2 -2x -2y

Answer 1

Lời giải:
a)

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

\(=(x+y)(x^2-y^2)=(x+y)(x+y)(x-y)=(x+y)^2(x-y)\)

b)

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

\(=x^2(y^2-1)-(y^2-1)=(x^2-1)(y^2-1)=(x-1)(x+1)(y-1)(y+1)\)c)

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

\(=(x-y)(x+y)-4(x-y)=(x-y)(x+y-4)\)

d)

\(x^2-y^2-2x-2y=(x^2-y^2)-(2x+2y)\)

\(=(x-y)(x+y)-2(x+y)=(x+y)(x-y-2)\)

Answer 2

Lời giải:
a)

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

\(=(x+y)(x^2-y^2)=(x+y)(x+y)(x-y)=(x+y)^2(x-y)\)

b)

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

\(=x^2(y^2-1)-(y^2-1)=(x^2-1)(y^2-1)=(x-1)(x+1)(y-1)(y+1)\)c)

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

\(=(x-y)(x+y)-4(x-y)=(x-y)(x+y-4)\)

d)

\(x^2-y^2-2x-2y=(x^2-y^2)-(2x+2y)\)

\(=(x-y)(x+y)-2(x+y)=(x+y)(x-y-2)\)