(x-1)(x-3)(x+1)(x+3)-20 因式分解要用拆项添项法

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(x-1)(x-3)(x+1)(x+3)-20 因式分解要用拆项添项法

(x-1)(x-3)(x+1)(x+3)-20 因式分解要用拆项添项法
(x-1)(x-3)(x+1)(x+3)-20 因式分解
要用拆项添项法

(x-1)(x-3)(x+1)(x+3)-20 因式分解要用拆项添项法
(x-1)(x-3)(x+1)(x+3)-20
=(x^2-1)(x^2-9)-20
=x^4-10x^2-11
=(x^2-11)(x^2+1)
=(x-√11)(x+√11)(x^2+1)

(x-1)(x-3)(x+1)(x+3)-20 =(x^2 1)(x^2-9)-20 = x^4-10x^2-11 = (x^2-11)(x^2+1) = (x+√11)(x-√11)(x^2+1).

(x-1)(x-3)(x+1)(x+3)-20

=[(x+1)(x-1)][(x+3)(x-3)]-20

=(x2-1)(x2-9)-20

=x4-x2-9x2+9-20

=x4-10x2-11

=(x2+1)(x2-11)

解析:

 利用公式: (a+b)(a-b)=a2-b2

 最后一部因式分解,对角相乘:

   x2     1

   x2    -11

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