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18(m-5)²-24(m-5)
18(m-5)²-24(m-5)
= (m-5)[18(m-5) - 24]
= 6(m-5)[3(m-5) - 4]
= 6(m-5)(3m-15-4)
= 6(m-5)(3m-19)
========================
2.3x(s-9)-12y(9-s)
3x(s-9) - 12y(9-s)
= 3x(s-9) + 12y(s-9)
= (s-9)(3x + 12y)
= 3(s-9)(x + 4y)
========================
3.1/36r²-3rs+81s²
1/36r² - 3rs + 81s²
= (r/6)² - 2(r/6)(9s) + (9s)²
= (r/6 - 9s)²
========================
4.25(2m-n)²-(4m+3n)²
25(2m-n)²-(4m+3n)²
= 25(4m² - 4mn + n²) - (16m² + 24mn + 9n²)
= 100m² - 100mn + 25n² - 16m² - 24mn - 9n²
= 84m² - 124mn + 16n²
= 4(21m² - 31mn + 4n²)
= 4(3m - 4)(7n - 1)
========================
5, c²-4x²+28xy-49y²
c² - 4x² + 28xy - 49y²
= c² - [(2x)² - 2(2x)(7y) + (7y)²]
= c² - (2x-7y)²
= [c - (2x-7y)][c + (2x-7y)] ..... 根據 a²-b²=(a-b)(a+b)
= (c-2x+7y)(c+2x-7y)
========================
6.49x²-21x+6y-4y²
49x² - 21x + 6y - 4y²
= (7x)² - (2y)² - 3(7x - 2y)
= [7x - 2y][7x + 2y] - 3(7x - 2y) ..... 根據 a²-b²=(a-b)(a+b)
= (7x-2y)(7x+2y-3)


2006-12-06 18:37:23 補充：
小小補充：factorization 常用的公式有：a²-b² = (a-b)(a+b)(a+b)² = a²+2ab+b²(a-b)² = a²-2ab+b²只是不用的項代入 a 和 b。

2006-12-06 19:13:42 補充：
Sorry, 第四題最後一行應該是= 4(3m - 4n)(7m - 1n)