【补基础题型】五种因式分解基础题

①:
4²-(x+y)²=(2+x+y)(2-x-y)
②:
ax-a-x+1=a(x-1)-(x-1)=(a-1)(x-1)
③:
ax+ax²-b-bx=x(ax-b)+(ax-b)=(x+1)(ax-b)
④9(a-b)²+12(a²-b²)+4(a+b)²=[3(a-b)]²+12(a+b)(a-b)+[2(a+b)]²=[3(a-b)+2(a+b)]²
=(3a-3b+2a+2b)²=(5a-b)²
⑤:
(x²+5x+3)(x²+5x-2)-6
=(x²+5x)²+(x²+5x)-12
=(x²+5x+4)(x²+5x-3)
=(x+1)(x+4)(x²+5x-3)