Toán Lớp 8: 1) Phân tích đa thức: a) 3xy(x-5)-6x(5-x) b) 3x^2(x+1)^2-x(x+1)^3

Question

Toán Lớp 8:  1) Phân tích đa thức: a) 3xy(x-5)-6x(5-x)                                       b) 3x^2(x+1)^2-x(x+1)^3                                       c)x^2-x+1/4                                       d) 8x^3-1/8

kimnguenoanh · Answer

a)   3xy(x - 5) - 6x(5 - x)   = 3xy(x - 5) + 6x(x - 5)   = (x - 5)(3xy + 6x)   = (x - 5) . 3x(y + 2)   b)   3x^2(x + 1)^2 - x(x + 1)^3   = (x + 1)^2(3x^2 - x(x + 1))   = (x + 1)^2 . x(3x - x - 1)   c)   x^2 - x + 1/4   = x^2 - 2 . x . 1/2 + 1/4   = (x - 1/2)^2   d)   8x^3 - 1/8   = (2x)^3 - (1/2)^3   = (2x - 1/2)(4x^2 + x + 1/4)

cobebongdem · Answer

a)3xy(x-5)-6x(5-x)   =3xy(x-5)+6x(x-5)   =(x-5)(3xy+6x)   =3x(x-5)(y+2)   b)3x&sup2;(x+1)&sup2;-x(x+1)&sup3;   =x(x+1)&sup2;[3x-(x+1)]   =x(x+1)&sup2;(3x-x-1)   =x(x+1)&sup2;(2x-1)   c)x&sup2;-x+1/4   =x&sup2;-2.x. 1/2+(1/2)^2   =(x-1/2)^2   &Aacute;p dụng HĐT:(A-B)&sup2;=A&sup2;-2AB+B&sup2;   d)8x&sup3;-1/8   =(2x)&sup3;-(1/2)^3   =(2x-1/2)[(2x)&sup2;+2x. 1/2+(1/2)^2]   =(2x-1/2)(4x&sup2;+x+1/4)   &Aacute;p dụng HĐT:A&sup3;-B&sup3;=(A-B)(A&sup2;+AB+B&sup2;)