问题 解答题

把下列各式因式分解

(1)2x2-4x                 

(2)a2b2-a2c2

(3)8a3b2-12ab3c+6a3b2c

(4)8a(x-a)+4b(a-x)-6c(x-a)

(5)-x5y3+x3y5

(6)(a+b)2-9(a-b)2                         

(7)-8ax2+16axy-8ay2

(8)5m(x-y)2+10n(y-x)3

(9)(a2+1)2-4a2

(10)m2+2n-mn-2m

(11)(a2-4a+4)-c2

(12)x2+6x-27                       

(13)9+6(a+b)+(a+b)2

(14)(x+3y)2+(2x+6y)(3y-4x)+(4x-3y)2

答案

(1)2x2-4x=2x(x-2);

(2)a2b2-a2c2

=a2(b2-c2),

=a2(b+c)(b-c);

(3)8a3b2-12ab3c+6a3b2c,

=2ab2(4a2-6bc+3a2c);

(4)8a(x-a)+4b(a-x)-6c(x-a),

=8a(x-a)-4b(x-a)-6c(x-a),

=2(x-a)(4a-2b-3c);

(5)-x5y3+x3y5

=x3y3(-x2+y2),

=x3y3(x+y)(-x+y);

(6)(a+b)2-9(a-b)2

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

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

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

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

(7)-8ax2+16axy-8ay2

=-8a(x2-2xy+y2),

=-8a(x-y)2

(8)5m(x-y)2+10n(y-x)3

=5(x-y)2[m-2n(x-y)],

=5(x-y)2(m-2nx+2ny);

(9)(a2+1)2-4a2

=(a2+1+2a)(a2+1-2a),

=(a+1)2(a-1)2

(10)m2+2n-mn-2m,

=(m2-mn)+(2n-2m),

=m(m-n)+2(n-m),

=(m-n)(m-2);

(11)(a2-4a+4)-c2

=(a-2)2-c2

=(a-2+c)(a-2-c);

(12)x2+6x-27=(x-3)(x+9);

(13)9+6(a+b)+(a+b)2

=32+2×3(a+b)+(a+b)2

=(a+b+3)2

(14)(x+3y)2+(2x+6y)(3y-4x)+(4x-3y)2

=(x+3y)2-2(x+3y)(4x-3y)+(4x-3y)2

=(x+3y-4x+3y)2

=(-3x+6y)2

=9(x-2y)2

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