问题 解答题
将下列各式分解因式
(1)3x-12x3
(2)2a(x2+1)2-2ax2
(3)2x2+2x+
1
2
(4)a2-b2-4a+4b
(5)20a2bx-45bxy2(6)x2+y2-1-2xy
(7)2m(a-b)-3n(b-a)(8)(a-b)(3a+b)2+(a+3b)2(b-a)
答案

(1)原式=3x(1-4x2

=3x(1-2x)(1+2x);

(2)原式=2a[(x2+1)2-x2]

=2x(x+12(x-1)2

(3)原式=2(x2+x+

1
4

=2(x+

1
2
2

(4)原式=(a2-b2)-(4a-4b)

=(a+b)(a-b)-4(a-b)

=(a-b)(a+b-4);

(5)原式=5bx(4a2-9y2

=5bx(2a-3y)(2a+3y);

(6)原式=(x2+y2-2xy)-1

=(x-y)2-1

=(x-y-1)(x-y+1);

(7)原式=2m(a-b)+3n(a-b)

=(a-b)(2m+3n);

(8)原式=(a-b)(3a+b)2-(a+3b)2(a-b)

=(a-b)[(3a+b)2-(a+3b)2]

=(a-b)(3a+b-a-3b)(3a+b+a+3b)

=(a-b)(2a-2b)(4a+4b)

=8(a-b)2(a+b).

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