F.2 three major identities

2007-11-02 8:01 pm
proofs of three major identities:
(a+b)(a-b)=a^2-b^2
(a+b)^2=a^2+2ab+b^2
(a-B)^2=a^2-2ab+b^2

回答 (3)

2007-11-07 2:22 am
✔ 最佳答案
1) (a+b)(a-b)≡a^2-b^2
L.H.S.=(a+b)(a-b)
=a^2-b^2 <--different of 2 squares
R.H.S.=a^2-b^2
∴It is identity.
2) (a+b)^2=a^2+2ab+b^2
L.H.S.=(a+b)^2
R.H.S.=a^2+2ab+b^2
=(a+b)^2 <---perfect square
∴It is identity.
3)L.H.S.=(a-b)^2
=a^2-2(a)(b)+b^2 <---perfect square
=a^2-2ab+b^2
R.H.S.=a^2-2ab+b^2
∴It is identity.
參考: me
2007-11-03 11:14 pm
(a+b)(a-b)=a^2-b^2
左方=(a+b)(a-b)
=a^2-b^2
左方=右方
∴((a+b)(a-b)≡a^2-b^2

(a+b)^2=a^2+2ab+b^2
左方=(a+b)^2
=a^2+2ab+b^2
左方=右方
∴((a+b)^2≡a^2+2ab+b^2

(a-B)^2=a^2-2ab+b^2
左方=(a-B)^2
=a^2-2ab+b^2
左方=右方
∴((a-B)^2≡a^2-2ab+b^2
2007-11-02 8:11 pm
(a+b)(a-b)≡a^2-b^2
L.H.S.=(a+b)(a-b)
=a(a-b)+b(a-b)
=a^2-ab+ab-b^2
=a^2-b^2
=R.H.S.
∴(a+b)(a-b)≡a^2-b^2

(a+b)^2≡a^2+2ab+b^2
L.H.S.=(a+b)^2
=(a+b)(a+b)
=a(a+b)+b(a+b)
=a^2+ab+ab+b^2
=a^2+2ab+b^2
=R.H.S.
∴(a+b)^2≡a^2+2ab+b^2

(a-b)^2≡a^2-2ab+b^2
L.H.S.=(a-b)^2
=(a-b)(a-b)
=a(a-b)-b(a-b)
=a^2-ab-ab+b^2
=a^2-2ab+b^2
=R.H.S.
∴(a-b)^2=a^2-2ab+b^2


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