Toán Lớp 8: Ptich các đa thức sau thành nhân tử : x^4-x^2+2x-1 x^4-4x^3-8x^2+8x x^3-4x^2-1 x^3+x^2y-xy^2-y^3 x^2y^2+1-x^2-y^2 x^3-y^3+3y-3x

Question

Toán Lớp 8:  Ptich các đa thức sau thành nhân tử :  x^4-x^2+2x-1 x^4-4x^3-8x^2+8x x^3-4x^2-1 x^3+x^2y-xy^2-y^3 x^2y^2+1-x^2-y^2  x^3-y^3+3y-3x

hauthanhyen98 · Answer

1/   x^4 - x^2 +2x -1   = (x^2)^2 -(x^2 -2x+1)   = (x^2)^2 - (x-1)^2   = (x^2-x+1)(x^2 +x-1)   2/   x^4 -4x^3 - 8x^2+8x   = x(x^3 - 4x^2 - 8x +8)   = x[ (x^3+8)  - (4x^2 -8x) ]   = x[ (x+2)(x^2 - 2x+4) - 4x(x+2)]   = x(x+2)(x^2 -6x+4)   3/   x^3 -4x^2  +4x -1   = (x^3 -1) - (4x^2 -4x)   = (x-1)(x^2 + x+1) -4x(x -1)   = (x-1)(x^2 -3x+1)   4/   x^3 +x^2y - xy^2 - y^3   = (x^3 +x^2y) - (xy^2+y^3)   = x^2(x + y) - y^2(x + y)   = (x^2-y^2)(x+y)   = (x-y)(x+y)(x+y)   = (x-y)(x+y)^2   5/   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)   6/   x^3 - y^3 +3y -3x   = (x-y)(x^2 + xy +y^2) - 3(x-y)   = (x-y)(x^2 +xy +y^2 -3)

buianhtuan · Answer

x^4 - x^2 + 2x - 1     = (x^2)^2 - (x^2 - 2x + 1)     = (x^2)^2 - (x - 1)^2     = (x^2 - x + 1)(x^2 + x - 1)     x^4 - 4x^3 - 8x^2 + 8x     = x(x^3 + 8 - 4x^2 - 8x)     = x[(x + 2)(x^2 - 2x + 4) - 4x(x + 2)]     = x(x + 2)(x^2 - 2x + 4 - 4x)     = x(x + 2)(x^2 - 6x + 4)     x^3 - 4x^2 + 4x - 1     = (x^3 - 1) - (4x^2 - 4x)     = (x - 1)(x^2 + x + 1) - 4x(x - 1)     = (x - 1)(x^2 + x + 1 - 4x)     = (x - 1)(x^2 - 3x + 1)     x^3 + x^2 y - 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)     x^2 y^2 + 1 - x^2 - y^2     = (x^2 y^2 - x^2) + (1 - y^2)     = x^2(y^2 - 1) - (y^2 - 1)     = (y^2 - 1)(x^2 - 1)     = (y - 1)(y + 1)(x - 1)(x + 1)     x^3 - y^3 + 3y - 3x     = (x - y)(x^2 + xy + y^2) - 3(x - y)     = (x - y)(x^2 + xy + y^2 - 3)