Question

分解因式 9a^2 x^4-4y^6 -x^4+16y^4 a^3-ab^2 16(a-b)^2-25(a+b)^2 a^2(a-b）+b^2(b-a) 4x^2-y^2+2x+y

Answer 1

解答：
(1)9a^2 x^4-4y^6=(3ax^2+2y^3)(3ax^2-2y^3)
(2)-x^4+16y^4 =-(x^2+4y^2)(x^2-4y^2)-(x^2+4y^2)(x+2y)(x-2y)
(3)a^3-ab^2 =a(a2-b^2)=a(a+b)(a-b)
(4)16(a-b)^2-25(a+b)^2 =[(4a-4b)+(5a+5b)][(4a-4b)-(5a+5b)]=-(9a+b)(a+9b)
(5)a^2(a-b）+b^2(b-a) =(a-b)(a^2-b^2)=(a-b)^2(a+b)
(6)4x^2-y^2+2x+y=(2x+y)(2x-y)+(2x+y)=(2x+y)(2x-y+1)