Question

计算两道数学题，急~

1.(16x^2+1)(4x^2+1)(2x+1)(1-2x)
2.(2+1）（2^2+1)(2^4+1)(2^8+1)(2^16+1)+1
1.(16x^4+1)(4x^2+1)(2x+1)(1-2x)
第一题是这样的……抱歉
2.(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)+1
第二题是这样的……抱歉

Answer 1

1

(16x^4+1)(4x^2+1)(2x+1)(1-2x)=(1+16x^4)(1+4x^2)[(1+2x)(1-2x)]=(1+16x^2)[(1+4x^2)(1-4x^2)]
=(1+16x^4)(1-16x^4)=)=1-256x^4

2

(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)+1=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)+1=(2^4-1)(2^4+1)(2^8+1)(2^16+1)+1
=(2^8-1)(2^8+1)(2^16+1)+1=(2^16-1)(2^16+1)+1=(2^32-1)+1
=2^32

3

9×11×101×10001=(10-1)(10+1)(10^2+1)(10^4+1)
=(10^2-1)(10^2+1)(10^4+1)=(10^4-1)(10^4+1)=10^8+1=100000001