因式分解 (1) 121(a-b)²-169(a+b)² (2) a(n-1)²-2a(n
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因式分解 (1) 121(a-b)²-169(a+b)² (2) a(n-1)²-2a(n-1)+a
![因式分解 (1) 121(a-b)²-169(a+b)² (2) a(n-1)²-2a(n](/uploads/image/z/19668364-52-4.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3+%281%29+121%EF%BC%88a-b%29%26%23178%3B-169%28a%2Bb%29%26%23178%3B+%282%29+a%28n-1%29%26%23178%3B-2a%28n)
(1)
121(a-b)²-169(a+b)²
=[11(a-b)]²-[13(a+b)²]
=[11(a-b)+13(a+b)][11(a-b)-13(a+b)]
=(24a+2b)(-2a-24b)
=-4(12a+b)(a+12b)
(2)
a(n-1)²-2a(n-1)+a
=a[(n-1)²-2(n-1)+1]
=a[(n-1)-1]²
=a(n-2)²
121(a-b)²-169(a+b)²
=[11(a-b)]²-[13(a+b)²]
=[11(a-b)+13(a+b)][11(a-b)-13(a+b)]
=(24a+2b)(-2a-24b)
=-4(12a+b)(a+12b)
(2)
a(n-1)²-2a(n-1)+a
=a[(n-1)²-2(n-1)+1]
=a[(n-1)-1]²
=a(n-2)²
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