因式分解(x+2)(x-2)+164(x+y)^2-20(x+y)+25a^2-b^2-4a+4b下面计算(2+1)(2^2+1)(2^4+1)……(2^(2n)+1)
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![因式分解(x+2)(x-2)+164(x+y)^2-20(x+y)+25a^2-b^2-4a+4b下面计算(2+1)(2^2+1)(2^4+1)……(2^(2n)+1)](/uploads/image/z/4340355-51-5.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%28x%2B2%29%28x-2%29%2B164%28x%2By%29%5E2-20%28x%2By%29%2B25a%5E2-b%5E2-4a%2B4b%E4%B8%8B%E9%9D%A2%E8%AE%A1%E7%AE%97%282%2B1%29%282%5E2%2B1%29%282%5E4%2B1%29%E2%80%A6%E2%80%A6%282%5E%282n%29%2B1%29)
因式分解(x+2)(x-2)+164(x+y)^2-20(x+y)+25a^2-b^2-4a+4b下面计算(2+1)(2^2+1)(2^4+1)……(2^(2n)+1)
因式分解
(x+2)(x-2)+16
4(x+y)^2-20(x+y)+25
a^2-b^2-4a+4b
下面计算
(2+1)(2^2+1)(2^4+1)……(2^(2n)+1)
因式分解(x+2)(x-2)+164(x+y)^2-20(x+y)+25a^2-b^2-4a+4b下面计算(2+1)(2^2+1)(2^4+1)……(2^(2n)+1)
(x+2)(x-2)+16
=x^2-4+16
=x^2+12
4(x+y)^2-20(x+y)+25
=(2x+2y-5)^2
a^2-b^2-4a+4b
=(a+b)(a-b)-4(a-b)
=(a-b)(a+b-4)
下面计算
(2+1)(2^2+1)(2^4+1)……(2^(2n)+1)
=(2-1)(2+1)(2^2+1)(2^4+1)……(2^(2n)+1)
=(2^2-1)(2^2+1)(2^4+1)……(2^(2n)+1)
=2^(4n)-1
[
x+2][x-2]+16=x2-4+16=x2+12