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因式分解是一种重要的恒等变形.对于一些数字计算题,如果能够巧妙、灵活地运用因式分解进行计算,可化难为易、化繁为简,简便、快捷地得到答案.一、运用提取公因式法进行计算例1计算:(1×2×3×4×6+…+n×2n×3n)/(1×5×10+2×10×20+…+n×5n×10n).解:原式=(1×2×3(1+2+3+…+n))/(1×5×10(1+2+3+…+n))=3/25.例2计算:(2008~3-2×2008~2-2006)/(2008~3+2008~2-2009).
Factorization is an important constant deformation. For some numerical calculation problems, if you can cleverly and flexibly use factorization to calculate, it can be difficult for the easy, simplistic, simple and quick to get the answer. First, Calculation using the common factor extraction method Example 1 Calculation: (1 × 2 × 3 × 4 × 6 + ... + n × 2n × 3n) / (1 × 5 × 10 + 2 × 10 × 20 + ... + n × 5n × 10n). Solution: Original = (1 × 2 × 3 (1 + 2 + 3 + ... + n)) / 1 × 5 × 10 (1 + 2 + 3 + ... + n) = 3/25 Example 2 Calculation: (2008 ~ 3-2 × 2008 ~ 2-2006) / (2008 ~ 3 + 2008 ~ 2-2009).