急!!!F.3 mathematics Questions

1) a^3+b^3-[(a^2)b]-ab^2
= (a+b)(a^2 - ab + b^2) - ab(a) - ab(b)
= (a+b)(a^2 - ab + b^2) - (a+b)ab
= (a+b)(a^2 - ab + b^2 - ab)
= (a+b)(a^2 - 2ab + b^2)
=(a+b)(a-b)^2
2) (1-cosθ)(1+cosθ)/[(tan^2)θ]
= (1^2 - cos^2θ) / (sinθ / cos θ)^2
= sin^2θ / sin^2θ * cos^2θ
= cos^2θ
3)
ㄥCAB = 30 , ㄥCBD = 48
CD / BD = tan48
BD = CD/tan48

CD / AD =
CD /( 150 + CD/tan48) = tan 30
CD = 150tan30 + CD (tan30/tan48)
CD (1 - tan30/tan48) = 150tan30
CD = 180.365... = 180.4m (4 sig.)





2009-08-03 21:51:30 補充：
For Q1 : If you have not learned that a^3 + b^3 = (a+b)(a^2 - ab + b^3),t
you should use the method as follow :

a^3+b^3-[(a^2)b]-ab^2

= a^3 - (a^2)b + b^3 - ab^2

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

= a^2 (a - b) - b^2(a - b)

= (a^2 - b^2) (a - b)

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

2009-08-03 21:52:28 補充：
For Q1 : If you have not learned that a^3 + b^3 = (a+b)(a^2 - ab + b^3),
you should use the method as follow :

a^3+b^3-[(a^2)b]-ab^2

= a^3 - (a^2)b + b^3 - ab^2

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

= a^2 (a - b) - b^2(a - b)

= (a^2 - b^2) (a - b)

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

2009-08-03 22:37:20 補充：
It should be a^3 + b^3 = (a+b)(a^2 - ab + b^2)