分解因式,就两题(1)abcx^2+(a^2b^2+c^2)x+abc(2)(a-b)x^2+2ax+a+b

Question

分解因式,就两题
(1)abcx^2+(a^2b^2+c^2)x+abc
(2)(a-b)x^2+2ax+a+b

Answer 1

(1)abcx^2+(a^2b^2+c^2)x+abc
=abcx^2+a^2b^2x+c^2x+abc
=abx(cx+ab)+c(cx+ab)
=(abx+c)(cx+ab)
(2)(a-b)x^2+2ax+a+b
=(a-b)x^2+2ax-a+b+2a
=(a-b)(x^2-1)+2ax+2a
=(a-b)(x+1)(x-1)+2a(x+1)
=(x+1)[(a-b)(x-1)+2a]
=(x+1)(ax-bx-a+b+2a)
=(x+1)(ax-bx+b+a)