五條數學題

1.a(x-y)^2+2a(x-y)^3
=a(x-y)^2[1+2(x-y)]
=a(x-y)^2(1+2x-2y)

2.8ax(2-3b)-2(3b-2)
=8ax(2-3b)+2(2-3b)
=2(2-3b)(4ax+1)

3.(2r-s+2)^2+s-2r-2
=(2r-s+2)^2-(2r-s+2)
=(2r-s+2)(2r-s+2-1)
=(2r-s+2)(2r-s+1)

4.x(x-y)^2-2(y-x)^3
=x(x-y)^2+2(x-y)^3
=(x-y)^2(x+2x-2y)
=(x-y)^2(3x-2y)

5.8(a+b)-20(a+b)^2
=4(a+b)[2-5(a+b)]
=4(a+b)(-5a-5b+2)



2009-11-20 22:41:22 補充：
樓上兩位, 第四題好像都錯了喔!

1. a(x-y)^2 + 2a(x-y)^3
= [a(x-y)^2] [1+2(x-y)]
= [a(x^2-2xy+y^2)] (1+2x-2y)
= (ax^2 - 2axy + ay^2) (1 + 2x - 2y)

2. 8x(2a-3ab)-(6b-4)
= 8ax(2-3b) - 2(3b-2)
= 8ax(2-3b) + 2(2-3b)
= (2-3b)(8ax+2)
= 2 (2 - 3b) (4ax + 1)

3. (2r-s+2)^2+s-2r-2
= (2r - s + 2)^2 - 2r + s - 2
= (2r - s + 2)^2 - (2r - s + 2)
= (2r - s + 2) (2r - s + 2 - 1)
= (2r - s + 2) (2r - s + 1)

4. x(x-y)^2-2(y-x)^3
= x (x - y)^2 + 2 (x - y)^3
= (x - y)^2 [x + 2(x - y)]
= (x - y)^2 (x + 2x - 2y)
= (x - y)^2 (3x - 2y)

5. 8(a+b)-20(a+b)^2
= 4 (a + b) [2 - 5(a + b)]
= 4 (a + b) (2 - 5a - 5b)

2009-11-20 22:39:44 補充：
Correction for Q.4
x(x-y)^2-2(y-x)^3
= x (x - y)^2 - 2 (x - y)^3
= (x - y)^2 [x - 2(x - y)]
= (x - y)^2 (x - 2x + 2y)
= (x - y)^2 (2y - x)

2009-11-20 22:41:45 補充：
Correction for Q.1
a(x-y)^2 + 2a(x-y)^3
= [a(x-y)^2] [1+2(x-y)]
= a (x - y)^2 (1 + 2x - 2y)

Check 下第4題

1)

a(x - y)^2 + 2a(x - y)^3

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

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

2)

8x(2a - 3ab) - (6b - 4)

= 8x(2a - 3ab) - 2(3b - 2)

= 2[4xa(2 - 3b) + 2(2 - 3b)]

= 2[(4xa + 2)(2 - 3b)

= 4(2xa + 1)(2 - 3b)

3)

(2r - s + 2)^2 + s - 2r - 2

= (2r - s + 2)(2r - s + 2) - (2r - s - 2)

= (2r - s + 2)(2r - s + 2 - 1)

= (2r - s + 2)(2r - s + 1)

4)

x(x - y)^2 - 2(y - x)^3

= x(x - y)(x - y) - 2(x - y)(x - y)(x - y)

= [(x - y)^2][x - 2(x - y)]

= [(x - y)^2][2y - x]


5)

8(a + b) - 20(a + b)^2

= 4[2(a + b) - 5(a + b)^2]

= 4[(a + b)(2 - 5(a + b)]

= 4(a + b)(2 - 5a - 5b)