Question

利用平方差公式计算、

利用平方差公式计算、
1. (a^4n+16) (a^2n+4) (a^n+2) (a^n-2)
2. (a-b+c-d) (a-b-c+d)
3. 997^2

Answer 1

1. (a^4n+16) (a^2n+4) (a^n+2) (a^n-2)=(a^4n+16) (a^2n+4) (a^2n-4)=)=(a^4n+16)(a^4n-16)=a^8n-16^2=a^8n-256

2. (a-b+c-d) (a-b-c+d)=[(a-b)+(c+d)][(a-b)-(c+d)]=(a-b)^2-(c+d)^2
3. 997^2=(1000-3)^2=1000^2-2*3*1000+3^2 =1000^2-6000+9

Answer 2

（注：为了更好计算，在前边乘以“2×1/2”，也就是乘以1） =2×(1-1/2)(1 1/2)(1 1/2^2)(1 1/2^4)(1 1/2^8) 1/2^15 =2×(

Answer 3

1.(a^4n+16)(a^2n+4)=(a^4n+16)(a^2n+4) (a^2n-4)=(a^4n+16)(a^4n-16)=(a^8n+256)

Answer 4

(a^4n+16) (a^2n+4) (a^n+2) (a^n-2)
=(a^4n+16) (a^2n+4) (a^2n-4)
=(a^4n+16) (a^4n-16)
=(a^8n-256)
(a-b+c-d) (a-b-c+d)
={(a-b)+(c-d)}{(a-b)-(c-d)}
={(a-b)^2-(c-d)^2}