(-a-b)^2=-a^2-2ab-b^2???

判別(-a-b)^2=-a^2-2ab-b^2是恆等式。
左方
=(-a-b)^2
=(-a-b)(-a-b)
=a^2+ab+ab+b^2
=a^2+2ab+b^2
右方
=a^2-2ab-b^2

∵左方≠右方
∴(-a-b)^2=-a^2-2ab-b^2不是恆等式

左=(-a-b)^2
=-(a+b)^2
=-(aa+2ab+bb)
=-a^2-2ab-b^2
右=-a^2-2ab-b^2
左=右
(-a-b)^2≡-a^2-2ab-b^2

( - a - b )^2 = - a^2 - 2ab - b^2 ???

L.H.S. = ( -a - b )^2
= [ - ( a + b ) ]^2
= (-1)^2 * ( a + b )^2
= (1) * ( a^2 + 2ab + b^2 )
=a^2 + 2ab + b^2
not equal to R.H.S. = - a^2 - 2ab - b^2
and
R.H.S. = - a^2 - 2ab - b^2
= - ( a^2 + 2ab + b^2 )
= - ( a + b )^2
not equal to L.H.S. = ( -a - b )^2

So that the above statement ( - a - b )^2 = - a^2 - 2ab - b^2 is not correct.

不對

(-a-b)^2
=((-1)(a+b))^2
=(a+b)^2
=a^2+2ab+b^2

2006-11-06 13:37:48 補充：
說簡單一點.. 只要將 -1 抽出來.. (-1)^2 就會抵消左.. (-a-b)^2 就等如 (a+b)^2 = a^2+2ab+b^2就好似 4^2 = (-4)^2 = 16 一樣