因式分解综合专项练习76题有答案Word文件下载.docx
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因式分解综合专项练习76题有答案Word文件下载.docx
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(22)6m(m+n)﹣4n(m+n)
(23)x4﹣y4
(24)﹣3a2+12ab﹣12b2.
(25)4a2﹣1
(26)2x3﹣12x2y+18xy2
(27)x2﹣2xy+y2﹣9
(28)ax2﹣16ay2
(29)a3+ab2﹣2a2b
(30)x2y(m﹣n)﹣xy2(n﹣m)
(31)a2+2ab+b2﹣9
(32)4x3﹣8x2+4x
(33)(x+y+z)2﹣(x﹣y﹣z)2
(34)(x﹣1)2﹣
(35)a2(x﹣y)﹣b2(x﹣y)
(36)2x2﹣12x+18
(37)2x3﹣18x
(38)x3y﹣x2y2﹣12xy3
(39)2x2﹣8xy+8y2;
(40)(x2+y2)2﹣4x2y2.
(41)(a﹣b)3﹣2(b﹣a)2
(42)3x3﹣12x2y+12xy2
(43)(3a﹣b)(x﹣y)+(a+3b)(y﹣x)
(44)2a2b+4ab﹣2b
(45)16x4﹣8x2y2+y4
(46)a3﹣6a2﹣7a
(47)(x2+x)2﹣(x+1)2
(48)﹣4x3y2+28x2y﹣2xy
(49)a3﹣4ab2
(50)(x2+1)2﹣4x(x2+1)+4x2
(51)x2y2﹣x2﹣4y2+4xy
(52)(a2+1)(a2+2)+
.
(53)a2﹣(b+c)2
(54)(x﹣y)(x2﹣xy+y2)﹣xy(x﹣y)
(55)x2+7x﹣18.
(56)4(x﹣2)2﹣1
(57)(x+y)2+4(x+y+1)
(58)2x(x﹣3)﹣8
(59)x2+y2﹣b2﹣2xy
(60)3a4bc﹣12a3b2c+12a2b3c,
(61)16(a﹣b)2﹣9(a+b)2,
(62)3x(a﹣b)﹣6y(b﹣a)
(63)a2+2a(b﹣c)+(b﹣c)2
(64)4ab2﹣4a2b﹣b3
(65)x3﹣2x2y+xy2
(66)x2﹣4y2﹣3x+6y
(67)x(x﹣y)﹣y(y﹣x)
(68)3a2﹣12b2
(69)m2(a﹣1)﹣2m(a﹣1)+(a﹣1)
(70)(a﹣b)2+4ab
(71)x2(a﹣b)+4(b﹣a)
(72)49(m+n)2﹣25(n﹣m)2
(73)(y﹣x)2﹣10x+10y+25
(74)a(x﹣a)(x+y)2﹣b(x﹣a)2(x+y)
(75)已知:
xy=2,x=2y+1.求:
x3y﹣4x2y2+4xy3的值.
(76)已知P=2x2+4y+13,Q=x2﹣y2+6x﹣1,比较代数式P,Q的大小.
因式分解综合76题参考答案:
=[3(a+b)+2(a﹣b)][3(a+b)﹣2(a﹣b)],
=(5a+b)(a+5b);
(2)(x2+y2)2﹣4x2y2,
=(x2+y2+2xy)(x2+y2﹣2xy),
=(x+y)2(x﹣y)2.
(5)ax2﹣16ay2
=a(x2﹣16y2)
=a(x+4y)(x﹣4y);
(6)﹣2a3+12a2﹣18a
=﹣2a(a2﹣6a+9)
=﹣2a(a﹣3)2;
(5)x2﹣7x+10=(x-2)(x﹣5);
(7)a2﹣2ab+b2﹣1
=(a﹣b)2﹣1
=(a﹣b+1)(a﹣b﹣1).
(7)﹣2xy﹣x2﹣y2,
=﹣(2xy+x2+y2),
=﹣(x+y)2;
=[4(m﹣n)+3(m+n)][4(m﹣n)﹣3(m+n)],
=(7m﹣n)(m﹣7n);
=4x2(x﹣y)﹣(x﹣y),
=(x﹣y)(4x2﹣1),
=(x﹣y)(2x+1)(2x﹣1).
(1)x3y﹣xy3
=xy(x2﹣y2)
=xy(x+y)(x﹣y);
=(a+1)(a2+2a+1)
=(a+1)3
=a2(x﹣y)﹣b2(x﹣y)
=(x﹣y)(a2﹣b2)
=(x﹣y)(a+b)(a﹣b);
=(x﹣
y)2﹣1
y+1)(x﹣
y﹣1).
=﹣3a(a2﹣4)
=﹣3a(a+2)(a﹣2);
=(x﹣y)(a2+4a+4)
=(x﹣y)(a+2)2.
=a2+3a﹣4
=(a+4)(a﹣1)
=x(x2﹣2x+1)
=x(x﹣1)2;
=8x2﹣16y2﹣7x2﹣xy+xy
=x2﹣16y2
=(x+4y)(x﹣4y).
=4(x2﹣16)
=4(x+4)(x﹣4);
=﹣b(4a2﹣4ab+b2)
=﹣b(2a﹣b)2;
=[4(m﹣n)+3(m+n)][4(m﹣n)﹣3(m+n)]
(22)x2(x﹣y)+(y﹣x)
=(x﹣y)(x+1)(x﹣1).
=2(m+n)(3m﹣2n);
=(x2+y2)(x2﹣y2)
=(x2+y2)(x+y)(x﹣y);
=﹣3(a2﹣4ab+4b2)
=﹣3(a﹣2b)2
=(2a+1)(2a﹣1);
=2x(x2﹣6xy+9y2)
=2x(x﹣3y)2;
(28)x2﹣2xy+y2﹣9
=(x﹣y)2﹣32
=(x﹣y+3)(x﹣y﹣3).
=a(x2﹣16y2)
=2(x+4y)(x﹣4y);
=a(a2+b2﹣2ab)
=a(a﹣b)2;
(31)x2y(m﹣n)﹣xy2(n﹣m)
=xy(m﹣n)(x+y);
=(a+b)2﹣9
=(a+b+3)(a+b﹣3).
=4x(x2﹣2x+1)
=4x(x﹣1)2;
=[(x+y+z)+(x﹣y﹣z)][(x+y+z)﹣(x﹣y﹣z)]
=4x(y+z).
(36)(x﹣1)2﹣
=(x﹣1+
)(x﹣1﹣
)
=(x﹣
)(x﹣
);
(37)a2(x﹣y)﹣b2(x﹣y)
=(x﹣y)(a2﹣b2)
=(x﹣y)(a+b)(a﹣b).
=2(x2﹣6x+9)
=2(x﹣3)2;
=2x(x2﹣9)
=2x(x+3)(x﹣3);
=yx(x2﹣xy﹣12y2)
=xy(x﹣4y)(x+3y).
=2(x2﹣4xy+4y2)
=2(x﹣2y)2;
=(x2+y2+2xy)(x2+y2﹣2xy)
=(a﹣b)2(a﹣b﹣2);
=3x(x2﹣4xy+4y2)
=3x(x﹣2y)2
=(x﹣y)[(3a﹣b)﹣(a+3b)]
=(x﹣y)(2a﹣4b)
=2(x﹣y)(a﹣2b).
(44)2a2b+4ab﹣2b=2b(a2+2a﹣1);
=(4x2﹣y2)2
=(2x+y)2(2x﹣y)2;
(47)a3﹣6a2﹣7a
=a(a2﹣6a﹣7)
=a(a﹣7)a+1);
=(x2+x+x+1)(x2+x﹣x﹣1)
=(x+1)2(x+1)(x﹣1)
=(x+1)3(x﹣1).
(49)﹣4x3y2+28x2y﹣2xy
=﹣2xy(2x2y﹣14x+1);
=a(a2﹣4b2)
=a(a+2b)(a﹣2b);
=(x2+1﹣2x)2
=(x﹣1)4
=(xy)2﹣(x﹣2y)2
=(xy+x﹣2y)(xy﹣x+2y)
=a4+3a2+
=(a2+
)2
=[a+(b+c)][a﹣(b+c)]
=(a+b+c)(a﹣b﹣c);
=(x﹣y)(x2﹣2xy+y2)
=(x﹣y)3;
=(x﹣2)(x+9).
=[2(x﹣2)+1][2(x﹣2)﹣1]
=(2x﹣3)(2x﹣5);
=(x+y+2)2;
=4x2﹣6x﹣8
=2(x﹣4)(x+1);
=(x﹣y)2﹣b2
=(x﹣y+b)(x﹣y﹣b).
=3a2bc(a2﹣4ab+4b2),
=3a2bc(a﹣2b)2;
=[4(a﹣b)+3(a+b)][4(a﹣b)﹣3(a+b)],
=(7a﹣b)(a﹣7b).
(1)4x2﹣64=4(x2﹣16)=4(x+4)(x﹣4);
=3(a﹣b)(x+2y);
=(a+b﹣c)2;
=﹣b(﹣4ab+4a2+b2)
=﹣b(2a﹣b)2
=x(x2﹣2xy+y2)
=x(x﹣y)2;
=(x+2y)(x﹣2y)﹣3(x﹣2y)
=(x﹣2y)(x+2y﹣3)
=(x﹣y)(x+y);
=3(a2﹣4b2)
=3(a+2b)(a﹣2b);
=(a﹣1)(m2﹣2m+1)
=(a﹣1)(m﹣1)2;
=a2﹣2ab+b2+4ab
=(a+b)2.
=x2(a﹣b)﹣4(a﹣b)
=(a﹣b)(x2﹣4)
=(a﹣b)(x+2)(x﹣2);
=[7(m+n)+5(n﹣m)][7(m+n)﹣5(n﹣m)]
=(7m+7n+5n﹣5m)(7m+7n﹣5n+5m)
=(2m+12n)(12m+2n)
=4(m+6n)(6m+n);
=(x﹣y)2﹣10(x﹣y)+25
=(x﹣y﹣5)2;
=(x﹣a)(x+y)(ax+ay﹣bx+ab).
(75)x3y﹣4x2y2+4xy3
=xy(x2﹣4xy+4y2)
=xy(x﹣2y)2
∵x=2y+1,
∴x﹣2y=1,
∴原式=2×
12=2.
(76)P﹣Q=(2x2+4y+13)﹣(x2﹣y2+6x﹣1)
=x2﹣6x+y2+4y+14
=x2﹣6x+9+y2+4y+4+1
=(x﹣3)2+(y+2)2+1
∵(x﹣3)2≥0,(y+2)2≥0,
∴P﹣Q=(x﹣3)2+(y+2)2+1≥1,
∴P>Q.
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