Maths~~~

1 (a^b)^c = a^(bc) a^b * a^c = a^(b+c) (ab)^c = a^c * b^c

2 (a+b)(c+d) = ac+ad+bc+bd

3

(x + 1/x) ^ 2 = 16

x^2 + 2 + 1/x^2 = 16

x^2 + 1/x^2 = 14.

(x-1/x)^2 = x^2 - 2 + 1/x^2 = 12.

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(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

(1-1/2^2)(1-1/3^2).......(1-1/10^2)

= (1+1/2)(1-1/2)......(1+1/10)(1-1/10)

= (3/2*4/3*...*11/10)(1/2*2/3*...*9/10)

= 11/2 * 1/10

= 11/20

1.幂的运算性质
同底数幂的乘法：am·an=am+n (m, n是自然数)
幂的乘方(am)n=amn，与积的乘方(ab)n=anbn
同底数幂的除法：am÷an=am-n (a≠0, m, n均为正整数，并且m>n)
a^0=1 (a≠0)

2 整式乘法法则
(a+b)(m+n)=am+an+bm+bn

3 已知x+1/x=4,
所以(x+1/x)^2=4
x^2+1/x^2+2=16
x^2+1/x^2=14
(x-1/x)^2＝x^2+1/x^2-2＝12
所以x^2+1/x^2＝14
(x-1/x)^2＝12