Question

分解因式，三题

(1)a4-a3+a2-a
(2)4a2-9b2+c2-4ac
(3)(ax+by)2(bx-ay)2

要求：使用初一水平，好的加分
三改成(ax+by)2+(bx-ay)2

Answer 1

a4-a3+a2-a
=a2(a2-a)+(a2-a)
=a(a-1)(a+1)(a2+1)
4a2-9b2+c2-4ac
=(4a2-4ac+c2)-9b2
=(2a-c)2-9b2
=(2a-c-3b)(2a-c+3b)
这个不需要分解了吧(ax+by)2(bx-ay)2

Answer 2

(1)a^4-a^3+a^2-a
=a^3(a-1)+a(a-1)
=(a-1)(a^3+a)
=a(a-1)(a^2+1)
(2)4a^2-9b^2+c^2-4ac
=(4a^2-4ac+c^2)-9b^2
=(2a-c)^2-(3b)^2
=(2a-c+3b)(2a-c-3b)
(3)(ax+by)^2+(bx-ay)^2
=(ax)^2+2abxy+(by)^2+(bx)^2-2abxy+(ay)^2
=(a^2+b^2)(x^2+y^2)

Answer 3

(1)a4-a3+a2-a
=a³(a-1)+a(a-1)
=a(a-1)(a²+1)
(2)4a2-9b2+c2-4ac
=4a²-4ac+c²-(3b)²
=(2a-c)²-(3b)²
=(2a-c+3b)(2a-c-3b)
(3)(ax+by)2-(bx-ay)2
=(ax+by+bx-ay)(ax+by-bx+ay)
=[(a+b)x+(b-a)y][(a-b)x+(a+b)y]

Answer 4

1.a(a-1)(a2+1)
2.(2a-c+3b)(2a-c-3b)