Question

请你利用所学的平方差公式求出2(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)-3^63

Answer 1

2(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)-3^63
=(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)-3^63
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)-3^63
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)-3^63
=(3^8-1)(3^8+1)(3^16+1)(3^32+1)-3^63
=(3^16-1)(3^16+1)(3^32+1)-3^63
=(3^32-1)(3^32+1)-3^63
=3^64-1-3^63
=3×3^63-3^63-1
=2×3^63-1

如果最后是x^64就好了
2(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)-3^64
=3^64-1-3^64
=-1

Answer 2

将2写成（3-1）你就可以用平方差公式化简了！