Math考考你2(難度升級**)

mn+4-2(m+n)
mn+4-2m-2n
(mn-2m)-(2n+4)
m(n-2)-2(n-2)
(n-2)(m-2)
____________________
ab^(2)-2c^(2)-bc(1-2a)
(ab^2-bc)+(2c^2-2abc)
b(ab-c)+2c(c-ab)
b(ab-c)+2c(ab-c)
(ab-c)(b+2c)
________________
p^(2)-q^(2)-p-q
(p+q)(p-q)-(p+q)
(p+q)(p-q-1)
________________
a^(2)b^(2)-4b^(2)-a^(2)+4
b^2(a^2-4)-(a-4)(a+4)
b^2(a-4)(a+4)-(a-4)(a+4)
(a-4)(a+4)(b-1)
_____________________
x^(2)-2x+1-y^(2)
(x-1)^2-y^2
(x+y-1)(x-y-1)
__________________
4a^(2)-b+2ab-1
(4a^2-1)-(b-2ab)
(2a+1)(2a-1)+b(2a-1)
(2a-1)(2a+b+1)
_____________________


2010-07-15 15:16:43 補充：
4a^(2)+a-4a^(3)-1
(4a^2-1)-(4a^3-a)
(2a+1)(2a-1)-a(4a^2-1)
(2a+1)(2a-1)-a(2a+1)(2a-1)
(1-a)(2a+1)(2a-1)

2010-07-15 15:17:16 補充：
x^(2)+y^(2)-z^(2)+2xy
(x+y)^2-z^2
(x+y+z)(x+y-z)

2010-07-15 15:18:53 補充：
Correction:
Q4
a^(2)b^(2)-4b^(2)-a^(2)+4
b^2(a^2-4)-(a-2)(a+2)
b^2(a-2)(a+2)-(a-2)(a+2)
(a-2)(a+2)(b^2-1)
(a-2)(a+2)(b-1)(b+1)

2010-07-21 17:07:30 補充：
ab^(2)-2c^(2)-bc(1-2a)
ab^2-2c^2-bc+2abc
(ab^2-bc)-(2c^2-2abc)
b(ab-c)-2c(c-ab)
b(ab-c)+2c(ab-c)
(b+2c)(ab-c)

1. mn+4-2(m+n)
step:
mn + 4 - 2m -2n
= mn -2m -2n +4
= m(n-2) -2(n-2)
=(m-2)(n-2)

2. ab^(2)-2c^(2)-bc(1-2a)
step:
ab^2 - 2c^2 -bc + 2abc
= ab^2 -c(2c-b) + 2abc
= ab^2 + 2abc - c(2c-b)
= ab(b+2c) + c ( b-2c)

3. p^(2)-q^(2)-p-q
step:
(p-q)(p+q)-(p+q)
=(p+q)(p-q-1)

4. a^(2)b^(2)-4b^(2)-a^(2)+4
(ab)^2 - (2b)^2 - a^2 + 2^2
=(b^2)(a-2)(a+2) - (a+2)(a-2)
=(a-2)(a+2) [ (b^2)-1 ]
=(a-2)(a+2) (b-1)(b+1)

5. x^(2)-2x+1-y^(2)
step:
x^2 - y^2 - 2x +1
= (x-y) (x+y) -2x + 1

or

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

6. 4a^(2)-b+2ab-1
step:
4a^2 + 2ab -b -1
= 2a(2a+b)-(b+1)
- not okay answer -
or

4a^2 -1 + 2ab -b
=(2a)^2 -1 + 2ab -b
=(2a-1)(2a+1) +b(2a-1)
=(2a-1) (2a+b+1)

7. 4a^(2)+a-4a^(3)-1
step:
4a^3 + 4a^2 + a -1
=4a^2 (a+1) + a -1
- not okay for answer -
or

4a^2 -1 + a - 4a^3
= (2a)^2 -1 + a( 1- 4a^2 )
= (2a + 1)(2a-1) + a ( 1- 2a) (1+2a)
= (2a+1) (2a-1 +a(1-2a))
= (2a+1) (2a-1 +a(2a -1) (-1))
= (2a+1) (2a-1 -a(2a-1))
= (2a+1) [(2a-1) (1-a) ]
= (2a+1) (2a-1) (1-a)

8. x^(2)+y^(2)-z^(2)+2xy
step:
x^2 - z^2 + y^2 + 2xy
= (x+z)(x-z) + y(y+2x)
- not okay for answer -

or

x^2 + 2xy + y^2 - z^2
= x(x+2y) + (y-z)(y+z)
- not okay for answer -

or

x^2 + 2xy + y^2 -z^2
= (x+y)^2 - z^2
= (x + y + z) (x + y -z)

2010-07-15 16:25:47 補充：
Q2 and Q5 both not okay for answering.