only一題因式分解..中一程度..

(x+1)² - (y+1)²
= x²+2x+1²-(y²-2y+1)
=x²+2x+1-y²+2y-1
=x²-y²+2x+2y

_______________________
(a+b)² = a²+2ab+b²
(a-b)² = a²-2ab+b²
(a+b) (a-b)=a²-b²

2008-05-10 15:01:18 補充：
(x+1)² - (y+1)²
= x²+2x+1²-(y²+2y+1)
=x²+2x+1-y²-2y-1
=x²-y²+2x-2y

(x+1)² - (y+1)²
=[(x)² +2(x)(1)+(1)² ]-[(y)² +2(y)(1)+(1)² ]
=[x² +2x+1]-[y² +2y+1]
=x² +2x+1-y² +2y+1
=x² +2x-y² -2y

(a+b)² = a²+2ab+b²
(a-b)² = a²-2ab+b²

因式分解:

(x+1)² - (y+1)²
=x²+2x+1-y²-2y-1
=x²-y²+2x-2y
=(x+y)(x-y)+2(x-y)
=(x-y)(x+y+2)


展開=令果條式變到最散
例子：

(x+y)²=x²+2xy+y²
(x-y)²=x²-2xy+y²
(x+y)^3=x^3+3x²y+3xy²+y^3
(x-y)^3=x^3-3x²y+3xy²-y^3
x^3+y^3=(x+y)(x²-xy+y²)
x^3-y^3=(x-y)(x²+xy+y²)
(ax+b)(cx+d)=acx+(ad+bc)x+bd
(x+y)(x-y)=x²-y²

2008-05-18 12:34:34 補充：
更多例子：

(a+b+c)²= a²+b²+c²+2ab+2ac+2bc
(x+a)(x+b)(x+c)= x^3+(a+b+c)x²+(ab+ac+bc)x+abc

因式分解:

(x+1)² - (y+1)²
=[(x+1)+(y+1)][(x+1)-(y+1)]
=(x+y+1)(x-y)

跟因式分解有關的公式

(a+b)^2 = a^2+2ab+b^2
(a-b)^2 = a^2-2ab+b^2
(a+b)^3 = a^2+2ab+b^2
a^3+b^3 = (a+b)(a^2-ab+b^2)
a^3-b^3 = (a-b)(a^2+ab+b^2)

(x+1)² - (y+1)²

=(x+1)(x+1)-(y+1)(y+1)

=x²+2-y²-2

=x²-y²

希望我解答是正確的

(x+1)^2 - (y+1)^2
=(x+1+y+1)(x+1-y-1)
=(x+y+2)(x-y)

因式分解和展開
完全平方和(a+b)^2= a^2+2ab+b^2
完全平方差(a-b)^2 = a)^2-2ab+b^2
平方差(a+b)(a-b)=a^2-b^2
立方和 (a+b)(a^2-ab+b^2)=a^3+b^3
立方差 (a-b)(a^2+ab+b^2)=a^3-b^3

Since a²-b² = (a+b)(a-b)
Therefore (x+1)² - (y+1)²
= [(x+1)+(y+1)] [(x+1)-(y+1)]
= (x+y+2)(x-y)

sample: (a-b)² = a²-2ab+b²
a²-b² = (a+b)(a-b)