s.2 maths

1. 計算812 – 192
812 - 192 = 620

2. 計算392 - 4(19)2
392 - 4(19)^2 =
392 - 1444 =
-1052

5. 把9f - 11e = 3ef的主項變為 e
9f - 11e = 3ef
9f = 3ef - 11e
9f = e (3f - 11)
9f / (3f - 11) = e
e = 9f / (3f - 11)

6. 展開 (2m - n)(7m - 8n +5)
(2m - n)(7m - 8n +5) =
(2m - n)(7m) - (2m - n)(8n) + (2m - n)(5) =
14m^2 - 7mn -16mn + 8n^2 + 10m - 5n =
14m^2 - 23mn + 10m + 8n^2 - 5n

7. 化簡
a) (1 + x2 - 2x) - ( x2 + 4x)
(1 + x2 - 2x) - ( x2 + 4x) =
1 + x^2 - 2x - x^2 - 4x =
1 - 6x

b) (x - 2y)(3x + y) + 2x(x - y)
(x - 2y)(3x + y) + 2x(x - y) =
(x - 2y)(3x ) - (x - 2y)(y) + 2x(x) - 2x(y) =
3x^2 - 6xy - xy - 2y^2 + 2x^2 - 2xy =
5x^2 - 9xy - 2y^2

11. 寫下書中三條恆等式。

Copy from your book.

12. 因式分解
a) p2r + pr - q2r – qr
p2r + pr - q2r – qr =
p^2 - q^2 + pr - qr =
(p + q)(p - q) + (r)(p - q) =
(p - q)(p + q + r)

b)(x - 2y)2 - x2
(x - 2y)2 - x2 =
[(x - 2) + x] [(x - 2) - x] =
[2x - 2][-2] =
[2(x - 1)][-2] =
-4 (x - 1)

c) 25h2 - (h2 +8h +16)
25h2 - (h2 +8h +16) =
(5)^2(h)^2 – [(h)^2 +2(h)(4) +(4)^2) =
(5h)^2 - (h + 4)^2 =
[(5h) + (h + 4)][(5h - (h + 4) ] =
[6h + 4][ 4h - 4] =
(2)(3h + 2) (4)(h - 1) =
8(3h + 2)(h - 1)

13. 展開
a) 3(x - y)(2x + 5y)
3(x - y)(2x + 5y) =
3(x - y)(2x) + 3(x - y)(5y) =
6x^2 - 6xy + 8xy - 5y^2 =
6x^2 - + 2xy - 5y^2

b) 3(x - y)(2x + 5y)(x - 4)
3(x - y)(2x + 5y)(x - 4) =
3(x - y)(2x + 5y)(x) - (3)(x - y)(2x + 5y)(4) =
(3x^2 - 3xy)(2x + 5y) - (12x - 12y)(2x + 5y) =
(3x^2 - 3xy)(2x) + (3x^2 - 3xy)(5y) - (12x - 12y)(2x) + (12x - 12y)(5y) =
6x^3 - 6x^2y +15x^2y + 15xy^2 - 24x^2 - 24xy + 60xy - 60y^2 =
6x^3 + 9x^2y + 15xy^2 - 24x^2 - 36xy - 60y^2 =
3(2x^3 + 3x^2y + 5xy^2 - 8x^2 - 12xy - 20y^2)