中四數學題!*

1. 4x² - 4xy + y²
= (2x - y)²

2. 4x²- 4xy + y²- 2x + y
= (2x - y)² - 2x + y
= (2x - y)² - (2x - y)
= (2x - y)(2x - y - 1)

3. a² - ab + 2a - 2b
2xy + 3 = 6x= a² + 2a - ab - 2b
= a(a+2) - b(a+2)
= (a-b)(a+2)

4. 169y² - 25
= (13y + 5) ( 13y -5)

5. x² - (y-z)²
= (x+y-z)(x-y+z)

6. 3b - ab
= b(3-a)

7. 9 - a²
= (3 +a)(3 - a)

8. 9 - a² + 3b - ab
= (3+a)(3-a) + 3b - ab
= (3+a)(3-a) + b(3-a)
= (3-a)(a+b+3)

主項變換 :

1. 令m成為公式mx = 2(m + c)的主項
mx = 2(m + c)
mx - 2m = 2c
m(x-2) = 2c
m= 2c/(x-2)

2. 令x成為公式b = 2x + (1 - x)a的主項
b = 2x + (1 - x)a
b = 2x - xa + a
b - a = x(2 - a)
x = (b - a)/(2 - a)

3. 若y = 2x + 3 , 以y表x
y = 2x + 3
y - 3 = 2x
x = (y-3)/2

4. 若2xy + 3 = 6x , 試以x表y
2xy + 3 = 6x
2xy - 6x = -3
2x(y - 3) = -3
y - 3 = -3/2x
y = 3 - (3/2x)
y= (6x - 3)/2x