(a-b)3 and (a+b)3 formula?
回答 (5)
2009-06-11 7:05 am
✔ 最佳答案
(a-b)^3=a^3-3a^2b+3ab^2-b^3(a+b)^3=a^3+3a^2b+3ab^2+b^3
2009-06-11 7:14 am
1)
(a - b)^3
= (a - b)(a - b)(a - b)
= (a*a - b*a - a*b + b*b)(a - b)
= (a^2 - ab - ab + b^2)(a - b)
= (a^2 - 2ab + b^2)(a - b)
= a^2*a - 2ab*a + b^2*a - a^2*b + 2ab*b - b^2*b
= a^3 - 2a^2b + ab^2 - a^2b + 2ab^2 - b^3
= a^3 - 2a^2b - a^2b + ab^2 + 2ab^2 - b^3
= a^3 - 3a^2b + 3ab^2 - b^3
2)
(a + b)^3
= (a + b)(a + b)(a + b)
= (a*a + b*a + a*b + b*b)(a + b)
= (a^2 + ab + ab + b^2)(a + b)
= (a^2 + 2ab + b^2)(a + b)
= a^2*a + 2ab*a + b^2*a + a^2*b + 2ab*b + b^2*b
= a^3 + 2a^2b + ab^2 + a^2b + 2ab^2 + b^3
= a^3 + 2a^2b + a^2b + ab^2 + 2ab^2 + b^3
= a^3 + 3a^2b + 3ab^2 + b^3
(a - b)^3
= (a - b)(a - b)(a - b)
= (a*a - b*a - a*b + b*b)(a - b)
= (a^2 - ab - ab + b^2)(a - b)
= (a^2 - 2ab + b^2)(a - b)
= a^2*a - 2ab*a + b^2*a - a^2*b + 2ab*b - b^2*b
= a^3 - 2a^2b + ab^2 - a^2b + 2ab^2 - b^3
= a^3 - 2a^2b - a^2b + ab^2 + 2ab^2 - b^3
= a^3 - 3a^2b + 3ab^2 - b^3
2)
(a + b)^3
= (a + b)(a + b)(a + b)
= (a*a + b*a + a*b + b*b)(a + b)
= (a^2 + ab + ab + b^2)(a + b)
= (a^2 + 2ab + b^2)(a + b)
= a^2*a + 2ab*a + b^2*a + a^2*b + 2ab*b + b^2*b
= a^3 + 2a^2b + ab^2 + a^2b + 2ab^2 + b^3
= a^3 + 2a^2b + a^2b + ab^2 + 2ab^2 + b^3
= a^3 + 3a^2b + 3ab^2 + b^3
2016-01-24 3:59 pm
ab
2009-06-11 7:04 am
(a-b)^3=a^3-b^3+3ab^2-3a^2b
(a+b)^3=a^3+b^3+3a^2b+3ab^2
(a+b)^3=a^3+b^3+3a^2b+3ab^2
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