Factorize(1+x)^4 - (1-x^2)^2
回答 (1)
2008-02-03 8:32 pm
✔ 最佳答案
(1+x)^4 - (1-x^2)^2=[(1+x)^2]^2 - (1-x^2)^2
=[(1+x)^2+(1-x^2)][(1+x)^2-(1-x^2)]
=(1+2x+x^2+1-x^2)(1+2x+x^2-1+x^2)
=(2x+2)(2x^2+2x)
=4(x+1)(x^2+x)
=4x(x+1)(x+1)
=4x(x+1)^2
2008-02-03 12:33:37 補充：
Remark: a^2 - b^2 = ( a + b )( a - b )
參考: My Maths Knowledge
收錄日期: 2021-04-25 19:57:41
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