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# 分解因式习题

14.3因式分解

(1)?x3z?x4y (2)3x(a?b)?2y(b?a)

1.?9x2y?3xy2?6xyz各项的公因式是( )

A.3y B.3xz C.?3xy D.?3x

2.a3b3?a2b3?ab分解因式得( )

A.ab(a2b2?ab2?1) B.ab(a2b2?ab2) C.a(a2b3?ab3?b) D.b(a3b2?a2b2?a)

3.下列各式:①x2?y2?(x?y)(x?y)②a(a?3b)?a2?3ab③4x2?3x?x(4x?3)

④x2?2x?2?(x?1)2?1,从左到右的变形中,是因式分解的是____________.

4.分解因式：4xn?1?10xn?_______________，x(x?y)?y(y?x)?_____________.

5.把下列各式分解因式:

(1)(a?2b)2?a(a?2b) (2)2a(x?y)?3b(y?x).

1.分解因式6xyz?4x2y2z2?2xz2时,应提取的公因式是( )

A.xyz B.2x C.2xy D.2xz

2.分解因式:2xm(x?y)m?1?4xm?1(x?y)m.

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14.3.2 公式法

1.下列各式中,能用平方差公式分解因式的有( )

①x2?y2;②x2?y2;③?x2?y2;④?x2?y2;⑤1?a2b2;⑥x2?81.

A.2个 B.3个 C.4个 D.5个

2.下列多项式能用完全平方公式分解因式的是( )

1①x2?4x?4;②4x2?4x?1;③x2?x?;④4m2?2mn?n2;⑤1?16a2;⑥(x?2y)2?2x?4y?1. 4

A.2个 B.3个 C.4个 D.5个

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3.a2?16a?64?____________________.

4.x2?ax?24在整数范围内可以分解因式,则整数a的值是________________.(只需填一个)

5.运用公式分解因式.

(1)49(a?b)2?16(a?b)2 (2)(x?y)2?10(x?y)?25

1.下列多项式中,能用公式法分解因式的是( )

A.x2?xy B.x2?xy C.x2?y2 D.x2?y2

2.若9a2?6(k?3)?a?1是完全平方式,则k的值为( )

A.?4 B.?2 C.3 D.4或2

3.把下列各式分解因式.

(1)16(x?y)2?25(x?y)2 (2)(m2?2m)2?2m(m?2)?1.

(1)ax?ay (2)6xyz?3xz2

(3)?x2z?z4y (4)36aby?12abx?6ab

(5)3x(a?b)?2y(b?a) (6)x(m?x)(m?y)?m(x?m)(y?m)

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(1)m2?2m?1 (2)9x2?12x?4

(3)1?10x?25x2 (4)(m?n)2?6(m?n)?9

(1)x2?7x?10 (2)x2?2x?8

(3)y2?7y?10 (4)x2?7x?18

(1)a2?b2?a?b (2)a2?b2?2ab?1

(3)(ax?by)2?(ay?by)2 (4)a2?2ab?b2?c2?2c?1

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1.若33n?27,32m?9,则3m?n?_________________.

2.已知a2?2a?3的值为0，则2a2?4a?5?________________.

3.a__________时，x2?2(a?1)x?49是完全平方式.

4.分解因式.

(1)7a2(16x?y)?7b2(y?16x) (2)(a?b)2?12(a?b)?36

15.已知,2x?y?,xy?2,求多项式2x4y3?x3y4的值. 3

1116.当a??1,b?2时,求[(a?b)2?(a?b)2](a2?2b2)的值. 222

17.先化简,再求值:4(x2?y)(x2?y)?(2x2?y)2]?y,其中x?,y?3. 2

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