Toán Lớp 8: phân tích đa thức thành nhân tử 1, 4x^2-y162+4x+1 2,x^3-x+y^3-y 3,x^2-x-y^2-y 4,x^2-2xy+y^2-z^2 5,x^4+2x^3+x^2

Question

Toán Lớp 8:  phân tích đa thức thành nhân tử 1, 4x^2-y162+4x+1 2,x^3-x+y^3-y 3,x^2-x-y^2-y 4,x^2-2xy+y^2-z^2 5,x^4+2x^3+x^2

trucoanh55 · Answer

1)   4x^2 - 16y^2 + 4x + 1    = (4x^2 + 4x + 1) - 16y^2    = (2x+1)^2 - (4y)^2    = (2x+1 - 4y)(2x+1+4y)   2)   x^3 - x + y^3 - y    = (x^3 + y^3) - (x+y)   =  (x+y)(x^2 - xy + y^2) - (x+y)   =  (x+y) (x^2 - xy  + y^2 - 1)   3)   x^2 - x - y^2 - y    = (x^2 - y^2) - (x+y)    = (x+y)(x-y) - (x+y)    = (x+y)(x-y-1)   4)   x^2 - 2xy + y^2 - z^2   =(x^2 -2xy+y^2)-z^2    = (x-y)^2 - z^2    = (x-y-z)(x-y+z)   5)   x^4 + 2x^3 + x^2    = x^2 (x^2 + 2x + 1)    = x^2 (x+1)^2

diemmyhoa · Answer

1)4x^2-y^2+4x+1   =(4x^2+4x+1)-y^2   =[(2x)^2+2.2x.1+1^2]-y^2   =(2x+1)^2-y^2   =(2x+1-y)(2x+1+y)   2)x^3-x+y^3-y   =(x^3+y^3)-(x+y)   =(x+y)(x^2-xy+y^2)-(x+y)   =(x+y)(x^2-xy+y^2-1)   3)x^2-x-y^2-y   =(x^2-y^2)-(x+y)   =(x-y)(x+y)-(x+y)   =(x+y)-(x-y-1)   4)x^2-2xy+y^2-z^2   =(x^2-2xy+y^2)-x^2   =(x-y)^2-x^2   =(x-y-z)(x-y+z)   5)x^4+2x^3+x^2   =x^2(x^2+2x+1)   =x^2(x+1)^2