急問F.1升F.2英數問題 20分

1.
(a)
3(x - 2)
= 3x - 6

(b)
2x(1 + x²)
= 2x + 2x³

(c)
-2(a + b - c)
= -2a - 2b + 2c

(d)
(x + 1)(x - 2)
= x(x - 2) + 1(x - 2)
= x² - 2x + x - 2
= x² - x + 2

(e)
(3x + 1)(2x² - 5x)
= 3x(2x² - 5x) + 1(2x² - 5x)
= 6x³ - 15x² + 2x² - 5x
= 6x³ - 13x² - 5x

(f)
(5x - y)²
= (5x - y)(5x - y)
= 5x(5x - y) - y(5x - y)
= 25x² - 5xy - 5xy + y²
= 25x² - 10xy + y²


2:
A = B + 1 … (1)
(1/2)B - (1/4)A = 1 … (2)

4 * (2):
4[(1/2)B - (1/4)A] = 4(1)
2B - A = 4 … (3)

Put (1) into (3):
2B - (B + 1) = 4
2B - B - 1 = 4
B = 5

(1): A = 5 + 1
A = 6


3:
(a)
x + 3 > 2
x + 3 - 3 > 2 - 3
x > -1

(b)
x - 2 < 3
x - 2 + 2 < 3 + 2
x < 5

(c)
7x - 9 > 9x + 7
9x + 7 < 7x - 9
9x + 7 - 7x - 7 < 7x - 9 - 7x - 7
2x < -16


4:(a)
(6ab)(-7a²b²)
= 6*(-7)*(a * a²) *(b * b²)
= -42a³b³

(b)
(-8a⁴b³)(-9a³b²)
= (-8) * (-9) * (a⁴ * a³) * (b³ * b²)
= 72a⁷b⁵

2010-08-21 14:03:44 補充：
4(b) 亂了碼。應是
(-8a^4 b^3)(-9a ^3 b^2)
= (-8) * (-9) * (a^4 * a^3) * (b^3 * b^2)
= 72 a^7 b^5

2010-08-23 01:26:57 補充：
偉程說得對，Q.1(d) 的答案應是：x² - x - 2

2010-08-23 16:26:23 補充：
Q.1 (d) 只是答案打錯了一個正負號，其餘各步驟均正確。

(d)
(x + 1)(x - 2)
= x(x - 2) + 1(x - 2)
= x² - 2x + x - 2
= x² - x + 2
有問題
= x² - 2x + x - 2
= x² - x - 2才對