分解因式:(1)4xy方-4x方y-y3次方(2)(4a方+1)方-16a方(3)(p-q)方+14(p-q)+49

题目

分解因式:(1)4xy方-4x方y-y3次方(2)(4a方+1)方-16a方(3)(p-q)方+14(p-q)+49
(4)(m+n)方-4(m方-n方)+4(m-n)方 (5)(x方-2x)方+2(x方-2x)+1 (6)2a方b+4ab-6b
(7)16x4次方-8x方y方+y的4次方
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答案

:(1)4xy方-4x方y-y3次方
=y(4xy-4x^2-y^2)
=-y(2x-y)^2
(2)(4a方+1)方-16a方
=16a^4 -8a^2 +1
=(4a^2- 1)^2
=(2a+1)^2(2a-1)^2
(3)(p-q)方+14(p-q)+49
=(p-q+7)^2
(4)(m+n)方-4(m方-n方)+4(m-n)方
=-7m^2 +n^2 +10mn
(5)(x方-2x)方+2(x方-2x)+1
=(x^2-2x +1)^2
=(x-1)^4
(6)2a方b+4ab-6b
=b(2a^2 +4a -6)
=2b(a+3)(a-1)
(7)16x4次方-8x方y方+y的4次方
=(4x^2-y^2)^2
=(2x+y)^2 (2x-y)^2
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