分解因式：（a^2+9b^2-1）^2-36a^2b^2.25x^2-4a^2+12ab-9ab^2分解因式（m^2-1）(n^2-1)+4mn

Question

分解因式：（a^2+9b^2-1）^2-36a^2b^2.25x^2-4a^2+12ab-9ab^2
分解因式（m^2-1）(n^2-1)+4mn

Answer 1

（a^2+9b^2-1）^2-36a^2b^2
=[(a^2+9b^2-1)-6ab][(a^2+9b^2-1)+6ab]
=[(a^2-6ab+9b^2)-1][(a^2+6ab+9b^2)-1]
=[(a-3b)^2-1][(a+3b)^2-1]
=(a-3b-1)(a-3b+1)(a+3b-1)(a+3b+1)
25x^2-4a^2+12ab-9b^2
=25x^2-(4a^2-12ab+9b^2)
=25x^2-(2a-3b)^2
=(5x-2a+3b)(5x+2a+3b)
（m^2-1）(n^2-1)+4mn
=m^2n^2-m^2-n^2+1+4mn
=m^2n^2+2mn+1-m^2+2mn-n^2
=(mn+1)^2-(m^2-2mn+n^2)
=(mn+1)^2-(m-n)^2
=(mn+1-m+n)(mn+1+m-n)