1.4a^2-b^2+6a-3b

1.4a^2-b^2+6a-3b
=(2a+b)(2a-b)+3(2a-b)
=(2a-b)(2a+b+1)
2.a^2（b^2-c^2）-c^2（b-c）（a+b）
=a^2（b+c）(b-c)-c^2（b-c）（a+b）
=(b-c)[a^2(b+c)-c^2(a+b)]
3.20x^2-43xy+14y^2
=(8x-7y)(5x-2y))
4.5x^2+4xy-28y^2
=(5x+14y)(x-2y)
5.20x^2-43xy+14y^2
=(8x-7y)(5x-2y))
6.3x^2+12x-5
=3(x+2)^2-17
=3(x+2+√51/3)(x+2-√51/3)
7.x^2+4x-4
=(x+2)^2-8
=(x+2+2√2)(x+2-2√2)
8.x^2-2xy-35y^2
＝(x-y)^2-(6y)^2
=(x+5y)(x-7y)
9.2x^2-7x-15
=(x-5y)(2x+3y)
10.x^4+2x^2-3
=(x^2+3)(x^2-1)
=(x^2+3)(x-1)(x+1)
11.(x+y)^2-3(x+y)+2
=(x+y-1)(x+y-2)
12.4x^2-12x+5
=(2x-5)(2x-1)
13.x^2+2-3x
=(x-1)(x-2)