國二乘法公式問題(急~~~~~~~~~~~`

1.
(a + b)² + (a - b)²
= (a² + 2ab + b²) + (a² - 2ab + b²)
= 2a² + 2b²
= 2(a² + b²)
= 2(3)
= 6


2.
5²/(5² - 1) * 6²/(6² - 1) * 7²/(7² - 1) * 8²/(8² - 1)
= 5² * 6² * 7² * 8² / [(5 + 1)(5 - 1) * (6 + 1)(6 - 1) * (7 + 1)(7 - 1) * (8 + 1)(8 - 1)]
= 5² * 6² * 7² * 8² / (6 * 4 * 7 * 5 * 8 * 6 * 9 * 7)
= 5² * 6² * 7² * 8² / (4 * 5 * 6² * 7² * 8 * 9)
= 5 * 8 / (4 * 9)
= 10/9


3.
265*263 + 266*266 - 266*264 - 264 *264
= (264 + 1)(264 - 1) + 266² - (265 + 1)(265 - 1) - 264²
= (264² - 1) + 266² - (265² - 1) - 264²
= 264² - 1 + 266² - 265² + 1 - 264²
= 266² - 265²
= (266 + 265)(266 - 265)
= 531


4.
a² - b²
= (a + b)(a - b)
= (4/3) * (1/5)
= 4/15


5.
(a + b)² - (a - b)² = 7² - 1²
(a² + 2ab + b²) - (a² - 2ab + b²) = 48
a² + 2ab + b² - a² + 2ab - b² = 48
4ab = 48
ab = 12

6.
99² = (99 + 1)(99 - 1) + a
99² = (99² - 1) + a
99² = 99² - 1 + a
-1 + a = 0
a = 1

(100 - 1)² = 100² - 200 + b
100² - 2(100)(1) + 1² = 100² - 200 + b
100² - 200 + 1 = 100² - 200 + b
b = 1

１.
(a+b)^2+(a-b)^2=2(a^2+b^2)=2*3=6

3.
令Y=266
==>265*263+266*266-266*264-264*264=(Y-1)(Y-3)+Y^2-Y(Y-2)-(Y-2)^2

=2Y=2*266=532
4.
a^2-b^2=(a+b)(a-b)=(4/3)*(1/5)=4/15

5.
解聯立知:a=4,b=3
==>a*b=12
6.
99^2=(99^2-1)+a=99^2+(-1+a)=(100-1)^2=100^2-200+1=100^2-200+b
==>a=1 ,b=1

2010-08-20 23:09:44 補充：
2.
[(5*5)/(5+1)(5-1)][(6*6)/(6+1)(6-1)][(7*7)/(7+1)(7-1)][(8*8)/(8+1)(8-1)]

=10/9

2010-08-20 23:32:04 補充：
抱歉打錯更正
3.

2Y-1=532-1=531