also (a+b)^3?
no proof required just answers is fine ty
maths: a^3 plus b^3?
2008-09-03 9:06 am
回答 (5)
2008-09-03 9:17 am
✔ 最佳答案
(a^3 + b^3)=(a+b)(a^2 -ab +b^2)_________________________________________________________
(a+b)^3=a^3 + 3a^2b + 3ab^2 +b^3
2008-09-03 4:16 pm
1)
x^3 + y^3 = (x + y)(x^2 - xy + y^2) (<== formula)
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
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
x^3 + y^3 = (x + y)(x^2 - xy + y^2) (<== formula)
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
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
2008-09-03 4:14 pm
uhm... what does a and b equal?
2008-09-03 4:11 pm
a^3+b^3=(a+b)(a^2-ab+b^2)
(a+b)^3=(a+b)(a^2+2ab+b^2)=
a^3+3a^2b+3ab^2+b^3
(a+b)^3=(a+b)(a^2+2ab+b^2)=
a^3+3a^2b+3ab^2+b^3
2008-09-03 4:09 pm
a^3 plus b^3 = a^3 + b^3
you cannot add both since they are not similar terms
on the other hand,
(a+b)^3 = a^3 + 3a^2 b + 3ab^2 + b^3
you cannot add both since they are not similar terms
on the other hand,
(a+b)^3 = a^3 + 3a^2 b + 3ab^2 + b^3
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