Question

20道因式分解计算题及答案

要过程,自己懒的找

Answer 1

1.因式分解3a^3b^2c－6a^2b^2c^2＋9ab^2c^3＝3ab^2 c(a^2-2ac+3c^2)
2.因式分解xy＋6－2x－3y＝(x-3)(y-2)
3.因式分解x^2(x－y)＋y^2(y－x)＝(x+y)(x-y)^2
4.因式分解2x^2－(a－2b)x－ab＝(2x-a)(x+b)
5.因式分解a^4－9a^2b^2＝a^2(a+3b)(a-3b)
8.因式分解ab(x^2－y^2)＋xy(a^2－b^2)＝(ay+bx)(ax-by)
9.因式分解(x＋y)(a－b－c)＋(x－y)(b＋c－a)＝2y(a-b-c)
10.因式分解a^2－a－b^2－b＝(a+b)(a-b-1)
11.因式分解(3a－b)2－4(3a－b)(a＋3b)＋4(a＋3b)2＝[3a-b-2(a+3b)]^2=(a-7b)^2
12.因式分解(a＋3)2－6(a＋3)＝(a+3)(a-3)1)x^2+2xy+y^2
2)x^2-y^2
1.a^4-4a+3
2.(a+x)^m+1*(b+x)^n-1-(a+x)^m*(b+x)^n
3.x^2+(a+1/a)xy+y^2
4.9a^2-4b^2+4bc-c^2
5.(c-a)^2-4(b-c)(a-b)
答案1.原式=a^4-a-3a+3=(a-1)(a^3+a^2+a-3)
2.[1-(a+x)^m][(b+x)^n-1]
3.(ax+y)(1/ax+y)
4.9a^2-4b^2+4bc-c^2=(3a)^2-(4b^2-4bc+c^2)=(3a)^2-(2b-c)^2=(3a+2b-c)(3a-2b+c)
5.(c-a)^2-4(b-c)(a-b)
= (c-a)(c-a)-4(ab-b^2-ac+bc)
=c^2-2ac+a^2-4ab+4b^2+4ac-4bc
=c^2+a^2+4b^2-4ab+2ac-4bc
=(a-2b)^2+c^2-(2c)(a-2b)
=(a-2b-c)^2

1.x^2+2x-8
2.x^2+3x-10
3.x^2-x-20
4.x^2+x-6
5.2x^2+5x-3
6.6x^2+4x-2
7.x^2-2x-3
8.x^2+6x+8
9.x^2-x-12
10.x^2-7x+10
11.6x^2+x+2
12.4x^2+4x-3