Question

phân tích các đa thức thành nhân tử

a)8x³+12x²y+6xy²+y³-z³

b)(4t+2)³+8(1-2t)³

c)x³+y³-z³+3xyz

Answer 1

a) `8x^3+12x^2y+6xy^2+y^3-z^3`

`=(8x^3+12x^2y+6xy^2+y^3)-z^3`

`=(2x+y)^3-z^3)`

`=(2x+y-z)[(2x+y)^2+(2x+y)z+z^2]`

`=(2x+y-z)(4x^2+4xy+y+2xz+yz+z^2)` 

b) `(4t+2)^3+8(1-2t)^3`

`=(4t+2)^3+(2-4t)^3`

`=(4t+2+2-4t)[(4t+2)^2-(4t+2)*(2-4t)+(2-4t)^2]`

`=4(16t^2+16t+4+16t^2-4+4-16t+16t^2)`

`=4(48t^2+4)`

c) `x^3+y^3-z^3+3xyz`

`=(x+y)^3-3xy(x+y)-z^3+3xyz`

`=(x+y)^3-z^3+[3xyz-3xy(x+y)]`

`=(x+y-z)(x^2+2xy+y^2+xz+yz+z^2)-3xy(x+y-z)`

`=(x+y-z)(x^2+2xy+y^2+xz+yz+z^2-3xy)`

`=(x+y-z)(x^2+y^2+z^2-xy+xz+yz)`