Toán Lớp 8: Phân tích đa thức thành nhân tử: a. 10x^4y^2-10x^3y^2-10x^2y^2+10xy^2 b. 25x^3-25x^2y-x+y c. x^2-6xy+9y^2+4x-12y d. x^2-xy +x^3-3x^2y+3

Question

Toán Lớp 8:  Phân tích đa thức thành nhân tử: a. 10x^4y^2-10x^3y^2-10x^2y^2+10xy^2 b. 25x^3-25x^2y-x+y c. x^2-6xy+9y^2+4x-12y d. x^2-xy +x^3-3x^2y+3xy^2-y^3

huongtructram · Answer

#Sad   a)    10x^4y^2-10x^3y^2-10x^2y^2+10xy^2     = 10xy^2(x^3-x^2-x+1)     = 10xy^2[(x^3-x^2)-(x-1)]     = 10xy^2[x^2(x-1)-(x-1)]     = 10xy^2(x^2-1)(x-1)     = 10xy^2(x-1)(x+1)(x-1)     = 10xy^2(x+1)(x-1)^2     b)     25x^3-25x^2y-x+y     = (25x^3-25x^2y)-(x-y)     = 25x^2(x-y)-(x-y)     = (x-y)(25x^2-1)     = (x-y)(5x-1)(5x+1)     c)     x^2-6xy+9y^2+4x-12y     = (x^2-6xy+9y^2)+(4x-12y)     = (x-3y)^2+4(x-3y)     = (x-3y)(x-3y+4)     d)     x^2-xy+x^3-3x^2y+3xy^2-y^3     = (x^2-xy)+(x^3-3x^2y+3xy^2-y^3)     = x(x-y)+(x-y)^3     = (x-y)[x+(x+y)^2]     = (x-y)(x+x^2+2xy+y^2)

aivilanlan · Answer

a)   10x^4 y^2 - 10x^3 y^2 - 10 x^2 y^2 + 10 xy^2   = 10xy^2 (x^3 - x^2 - x + 1)   =  10xy^2 [ x^2 (x-1) - (x-1)]   =  10xy^2 (x^2-1)(x-1)    = 10xy^2 (x+1)(x-1)(x-1)   =  10xy^2 (x+1) (x-1)^2   b)   25x^3 - 25x^2y - x + y    = 25x^2 (x-y) - (x-y)   =  (25x^2 - 1)(x-y)   =  [ (5x)^2 - 1^2] (x-y)    = (5x-1)(5x+1)(x-y)   c)   x^2 - 6xy + 9y^2 + 4x- 12y    =  (x^2 - 2 . x . 3y + (3y)^2] + 4 (x-3y)    = (x-3y)^2 + 4 (x-3y)    = (x-3y)(x-3y+4)   d)   x^2 - xy + x^3 - 3x^2y + 3xy^2 - y^3    = (x^2 - xy) + (x^3 - 3x^2y +3xy^2-  y^3)   =  x (x-y) + (x-y)^3   =  (x-y) [ x + (x-y)^2]    = (x-y)(x + x^2 - 2xy + y^2)