f.2 maths (20點)

1a x3+27
=x^3+3^3
=(x+3)(x^2-3x+9)....因為有條identity係x^3+y^3=(x+y)(x^2-xy+y^2)
1b x3-7x+6
=x^3-7x+6-21+21....加入(-21+21)有助解決算式
=x^3+27-7x-21
=(x+3)(x^2-3x+9)-7(x+3)
=(x+3)(x^2-3x+9-7)
=(x+3)(x^2-3X+2)
2 20000*(1+6%)
=$21200
3 ab(p2+1)-p(a2 + b2 )
=abp^2+ab-a^2p-pb^2....將ab乘入(p^2+1)同p乘入(a^2+b^2)
=ap(bp-a)-b(bp-a)
=(ap-b)(bp-a)
4 10xy(z2+1)-2z(25x2+y)
=10xyz^2+10xy-50x^2z-2zy....同第3題差唔多
=10xz(zy-5x)-2(zy-5xy)
=(10xz-2)(2y-5x)
5a 993x996+4x993+7x996+28
=993x(996+4)+7x(996+4)
=993x1000+7x1000
=1000x(993+7)
=1000x1000
=1000000
5b 123 x 321 + 123 x 179 - 73 x 321 - 73 x 179
=123x(321+179)-73x(321+179)
=123x500-73x500
=500x(123-73)
=500x50
=25000

5a 993 x 996 + 4 x 993 + 7 x 996 +28
= 993 x (996 + 4) + 7 x (996 + 4)
=993 x 1000 + 7 x 1000
= 1000 x (993 + 7)
= 1000 x 1000
= 1000000

5b. 123 x 321 + 123 x 179 - 73 x 321-73 x 179
=123 x (321 + 179) - 73 x (321 + 179)
=123 x 500 - 73 x 500
=(123 - 73) x 500
=50 x 500
=25000

2009-04-15 10:04:51 補充：
其餘題目因打唔出二次方及三次方，故沒有打出來，請各位C HING指教吓點樣可以打到。