Question

因式分解题3道大神们帮帮忙

4X二次方-4X-Y二次方+4Y-3 2X二次方-XY-6Y二次方+7X+7Y+3 X四次方+X三次方-3X二次方-4X-4

Answer 1

①4x^2-4x-y^2+4y-3 =4x^2-4x-y^2+4y+1-4 =4x^2-4x+1-y^2+4y-4 =(2x-1)^2-(y^2-4y+4) =(2x-1)^2-(y-2)^2 =(2x-1+y-2)(2x-1-y+2) =(2x+y-3)(2x-y+1) ②待定系数法的经典例子 2x^2-xy-6y^2+7x+7y+3 ＝(x-2y+m)(2x+3y+n) ＝2x^2-xy-6y^2+(2m+n)x+(3m-2n)y+mn 2m+n=7 3m-2n=7 mn=3 m=3 n=1 所以 原式＝(x-2y+3)(2x+3y+1) ③x^4+x^3-3x^2-4x-4 =(x^4+x^3+x^2)-4x^2-4x-4 =x^2(x^2+x+1)-4(x^2+x+1) =(x^2+x+1)(x^2-4) =(x^2+x+1)(x+2)(x-2)