Question

进行因式分解①2mn-m²-n²②9-1/16a²③（a²+1）²-4

Answer 1

1.2mn-m²-n²=-（-2mn+m²+n²）=-（m+n)^2

2.9-1/16a²=3^2-(1/4a)^2=(3+1/4a)(3-1/4a)

3.（a²+1）²-4a²=(a^2+1-2a)(a^2+1+2a)=(a-1)^2(a+1)^2

④（x²+4）²-16x²=(x^2+4x+4)(x^2-4x+4)=(x+2)^2(x-2)^2

5.621²-148²-769*373=(621+148)(621-148)-769*373=769*473-769*373=76900

6.m²-2mn+n²-16m²n² =(m-n)^2-(4mn)^2=(m-n+4mn)(m-n-4mn)