Question

添项法因式分解例题

用分组法拆项添项法因式分解下列题目
4x^2-y^2+2x-y
x^4 y+2x^3 y^2-x^2 y-2xy^2
x^3-8y^3-x^2-2xy-4y^2
x^2+x-(y^2+y)
ab(x^2-y^2)+xy(a^2-b^2)

Answer 1

原式=(4x^2-y^2)+2x-y
=(2x+y)(2x-y)+(2x-y)
=(2x-y)(2x+y+1)
x^4 y+2x^3 y^2-x^2 y-2xy^2
=(x^4 y-x^2 y)+(2x^3 y^2-2xy^2)
=x^2 y(x+1)(x-1)+2xy^2(x+1)(x-1)
xy(x+1)(x-1)(x+2y)
x^3-8y^3-x^2-2xy-4y^2
=(x^3-8y^3)-(x^2+2xy+4y^2)
=(x-2y)(x^2+2xy+4y^2)-(x^2+2xy+4y^2)
=(x^2+2xy+4y^2)(x-2y-1)
x^2+x-(y^2+y)
=x^2+x-y-y^2
=(x+y)(x-y)+(x-y)
=(x-y)(x+y+1)
ab(x^2-y^2)+xy(a^2-b^2)
=abx^2-aby^2+xya^2-xyb^2
=(abx^2-xyb^2)+(xya^2-aby^2)
=xb(ax-yb)+ay(ax-yb)
=(ax-yb)(xb+ay)
累死我了~
题不算难但打出来就难了（这题绝对不需要悬赏30分啊~）
我是初2的学生,所以如果错了或没对的.别怪我~
最好验算一下