MATHS(FACTORIZATION)
回答 (7)
2006-10-27 6:14 am
✔ 最佳答案
(a+b)^3+(a-b)^3 =(a+b+a-b)[(a+b)^2-(a+b)(a-b)+(a-b)^2]
=2a(a^2+2ab+b^2-a^2+b^2+a^2-2ab+b^2)
=2a(a^2+3b^2)
2006-10-31 8:34 am
(a+b)^3+(a-b)^3
=a^3+3a^2b+3ab^2+b^3+a^3-3a^2b+3ab^2-b^3
=2a^3+6ab^2
=2a(a^2+3b^2)
=a^3+3a^2b+3ab^2+b^3+a^3-3a^2b+3ab^2-b^3
=2a^3+6ab^2
=2a(a^2+3b^2)
參考: 自己
2006-10-28 11:45 pm
(a+b)^3+(a-b)^3
=(a+b+a-b)(a^2+2ab+b^2-a^2+b^2+a^2-2ab+b^2)
=2a(2a^2+3b^2-a^2)
=2a(a^2+3b^2)
=(a+b+a-b)(a^2+2ab+b^2-a^2+b^2+a^2-2ab+b^2)
=2a(2a^2+3b^2-a^2)
=2a(a^2+3b^2)
2006-10-27 7:30 am
=(a+b)(a^2+2ab+b^2)+(a-b)((a^2-2ab+b^2)
=a^3+2a^2b+ab^2+a^2b+2ab^2+b^3+
a^3-2a^2b+ab^2-a^2b+2ab^2-b^3
=a^3+ab^2++2ab^2+a^3+ab^2++2ab^2
=2a^3+6ab^2
=2a(a^2+3b^2)
=a^3+2a^2b+ab^2+a^2b+2ab^2+b^3+
a^3-2a^2b+ab^2-a^2b+2ab^2-b^3
=a^3+ab^2++2ab^2+a^3+ab^2++2ab^2
=2a^3+6ab^2
=2a(a^2+3b^2)
2006-10-27 7:11 am
(a+b)^3+(a-b)^3
=(a+b+a-b)[(a+b)^2-(a+b)(a-b)+(a-b)^2]
=2a(a^2+2ab+b^2-a^2+b^2+a^2-2ab+b^2)
=2a(a^2+3b^2)
=(a+b+a-b)[(a+b)^2-(a+b)(a-b)+(a-b)^2]
=2a(a^2+2ab+b^2-a^2+b^2+a^2-2ab+b^2)
=2a(a^2+3b^2)
2006-10-27 6:44 am
=(a+b)(a+b)(a+b)+(a-b)(a-b)(a-b)
=((a+b)a+(a+b)b)(a+b)+((a-b)a-(a-b)b)
=(a^2+ab+ab+b^2)+(a^2-ab-ab-b^2)
=a^4+2ab+b^2-2ab-b^2
=a^4
=((a+b)a+(a+b)b)(a+b)+((a-b)a-(a-b)b)
=(a^2+ab+ab+b^2)+(a^2-ab-ab-b^2)
=a^4+2ab+b^2-2ab-b^2
=a^4
2006-10-27 6:18 am
(a+b)^3 + (a-b)^3
= [ (a+b) + (a-b) ] [ (a+b)^2 - (a+b)(a-b) + (a-b)^2 ]
= (2a) [ (a^2 + 2ab + b^2) - (a^2 - b^2) + (a^2 - 2ab + b^2) ]
= 2a ( a^2 + 3b^2 )
= [ (a+b) + (a-b) ] [ (a+b)^2 - (a+b)(a-b) + (a-b)^2 ]
= (2a) [ (a^2 + 2ab + b^2) - (a^2 - b^2) + (a^2 - 2ab + b^2) ]
= 2a ( a^2 + 3b^2 )
收錄日期: 2021-04-12 22:28:05
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