因式分解：1.4b^2-a^2+a+2b2.4b^2-a^2+1+4b3.(a-2b)^2+3a-6b-104.a^4-a^2-25.a(a^2-b^2)-b(a+b)(a+3b)6.(x^2+4x)(x^2+4x-1)-207.a^2-b^2-2bc-c^28.x^5-3x^3y^2+2xy^4

Question

因式分解：
1.4b^2-a^2+a+2b
2.4b^2-a^2+1+4b
3.(a-2b)^2+3a-6b-10
4.a^4-a^2-2
5.a(a^2-b^2)-b(a+b)(a+3b)
6.(x^2+4x)(x^2+4x-1)-20
7.a^2-b^2-2bc-c^2
8.x^5-3x^3y^2+2xy^4

Answer 1

1.4b^2-a^2+a+2b
=(2b+a)(2b-a)+(2b+a)
=(2b+a)(2b-a+1)
2.4b^2-a^2+1+4b
=(4b^2+4b+1)-a^2
=(2b+1)^2-a^2
=(2b+a+1)(2b-a+1)
3.(a-2b)^2+3a-6b-10
=(a-2b)^2+3(a-2b)-10
=(a-2b+5)(a-2b-2)
4.a^4-a^2-2
=(a^4-1)-(a^2+1)
=(a^2+1)(a^2-1)-(a^2+1)
=(a^2+1)(a^2-1-1)
=(a^2+1)(a^2-2)
5.a(a^2-b^2)-b(a+b)(a+3b)
=a(a-b)(a+b)-b(a+b)(a+3b)
=(a+b)(a^2-ab-ab-3b^2)
=(a+b)(a^2-2ab-3b^2)
=(a+b)(a-3b)(a+b)
=(a+b)^2(a-3b)
6.(x^2+4x)(x^2+4x-1)-20
=(x^2+4x)[(x^2+4x)-1]-20
=(x^2+4x)^2-(x^2+4x)-20
=(x^2+4x-5)(x^2+4x+4)
=(x+5)(x-1)(x+2)^2
7.a^2-b^2-2bc-c^2
=a^2-(b^2+2bc+c^2)
=a^2-(b+c)^2
=(a+b+c)(a-b-c)
8.x^5-3x^3y^2+2xy^4
=x(x^4-3x^2y^2+2y^4)
=x(x^2-2y^2)(x^2-y^2)
=x(x^2-2y^2)(x+y)(x-y)