Toán Lớp 8: 3x^2-22xy-4x+8y+7y^2+1 12x ^ 2 +5x−12y ^2 +12y−10xy−3

Question

Toán Lớp 8:  3x^2-22xy-4x+8y+7y^2+1 12x ^ 2  +5x−12y ^2 +12y−10xy−3

baoquyen · Answer

Giải đáp:   a)(x-7y-1)(3x-y-1)   b)(2y+3x-1)(4x-6y+3)   Lời giải và giải thích chi tiết:   a)3x&sup2;-22xy-4x+8y+7y&sup2;+1   =3x&sup2;-21xy-xy-3x-x+7y+y+7y&sup2;+1   =(3x&sup2;-21xy-3x)-(xy-7y&sup2;-y)-(x-7y-1)   =3x(x-7y-1)-y(x-7y-1)-(x-7y-1)   =(x-7y-1)(3x-y-1)   b)12x&sup2;+5x-12y&sup2;+12y-10xy-3   =12x&sup2;+9x-4x-12y&sup2;+6y+6y+8xy-18xy-3   =-(12y&sup2;+18xy-6y)+(8xy+12x&sup2;-4x)+(6y+9x-3)   =-6y(2y+3x-1)+4x(2y+3x-1)+3(2y+3x-1)   =(2y+3x-1)(4x-6y+3)

kimnguenoanh · Answer

@Kem     3x^2-22xy-4x+8y+7y^2+1    Giả sử:  (A= left(3x+ay+b right) left(x+cy+d right) )      (=3x^2+3cxy+3dx+axy+acy^2+ady+bx+bcy+bd )      (=3x^2+acy^2+ left(3c+a right)xy+ left(3d+b right)x+ left(ad+bc right)y+bd )    Ta c&oacute;:  ( begin{cases} begin{matrix}ac=-7  3c+a=-22  3d+b=-4  ad+bc=8 end{matrix}  bd=1 end{cases} )   ( Rightarrow begin{cases}a=-1  b=-1  c=-7  d=-1 end{cases} )    Vậy   (A= left(3x-y-1 right) left(x-7y-1 right) )    ______________________________________________________________________    12x^2 + 5x - 12y&sup2; + 12y - 10xy - 3      = (12x^2 - 18xy + 9x) - (4x - 6y + 3) + (8xy - 12y^2 + 6y)      = 3x(4x - 6y + 3) - (4x - 6y + 3) + 2y(4x - 6y + 3)      = (4x - 6y + 3)(3x + 2y - 1)