将下列各式分解因式（1)1-x²+4xy-4y²(2)(x²+9)-36x²(3)4(a+3)²-12m(a+3)+9m²(4)2x²+2x+1/2(5)(a-9)(a+1)+25(6)4(a+3b)²-(a-3b)²(7)(a²+9)(b-5)+(4a-5)(5-b)

Question

将下列各式分解因式
（1)1-x²+4xy-4y²
(2)(x²+9)-36x²
(3)4(a+3)²-12m(a+3)+9m²
(4)2x²+2x+1/2
(5)(a-9)(a+1)+25
(6)4(a+3b)²-(a-3b)²
(7)(a²+9)(b-5)+(4a-5)(5-b)

Answer 1

（1)1-x²+4xy-4y²
=1-(x-2y)²
=(1+x-2y)(1-x+2y)
(2)(x²+9)-36x² 确定题没错?
=9-35x²
=(3-√35x)(3+√35x)
(3)4(a+3)²-12m(a+3)+9m²
=[2(a+3)-3m]²
=(2a-3m+6)²
(4)2x²+2x+1/2
=2(x+1/2)²
(5)(a-9)(a+1)+25
=a²-8a-9+25
=a²-8a+16
=(a-4)²
(6)4(a+3b)²-(a-3b)²
=[2(a+3b)-(a-3b)][2(a+3b)+(a-3b)]
=(a+9b)(3a+3b)
=3(a+9b)(a+b)
(7)(a²+9)(b-5)+(4a-5)(5-b)
=(a²+9)(b-5)-(4a-5)(b-5)
=(b-5)(a²+9-4a+5)
=(b-5)(a²-4a+14)