根据多项式乘法法则有(a+b)(a²-ab+b²)=a³-a²b+ab²+a²b-ab²+b³=a³+b³即(a+b)(a²-ab+b²)=a³+b³又因为分解因式与整式乘法之间存在互逆关系,所以a³+b&
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![根据多项式乘法法则有(a+b)(a²-ab+b²)=a³-a²b+ab²+a²b-ab²+b³=a³+b³即(a+b)(a²-ab+b²)=a³+b³又因为分解因式与整式乘法之间存在互逆关系,所以a³+b&](/uploads/image/z/3743040-48-0.jpg?t=%E6%A0%B9%E6%8D%AE%E5%A4%9A%E9%A1%B9%E5%BC%8F%E4%B9%98%E6%B3%95%E6%B3%95%E5%88%99%E6%9C%89%28a%2Bb%29%28a%26%23178%3B-ab%2Bb%26%23178%3B%29%3Da%26%23179%3B-a%26%23178%3Bb%2Bab%26%23178%3B%2Ba%26%23178%3Bb-ab%26%23178%3B%2Bb%26%23179%3B%3Da%26%23179%3B%2Bb%26%23179%3B%E5%8D%B3%EF%BC%88a%2Bb%EF%BC%89%EF%BC%88a%26%23178%3B-ab%2Bb%26%23178%3B%29%3Da%26%23179%3B%2Bb%26%23179%3B%E5%8F%88%E5%9B%A0%E4%B8%BA%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F%E4%B8%8E%E6%95%B4%E5%BC%8F%E4%B9%98%E6%B3%95%E4%B9%8B%E9%97%B4%E5%AD%98%E5%9C%A8%E4%BA%92%E9%80%86%E5%85%B3%E7%B3%BB%2C%E6%89%80%E4%BB%A5a%26%23179%3B%2Bb%26)
根据多项式乘法法则有(a+b)(a²-ab+b²)=a³-a²b+ab²+a²b-ab²+b³=a³+b³即(a+b)(a²-ab+b²)=a³+b³又因为分解因式与整式乘法之间存在互逆关系,所以a³+b&
根据多项式乘法法则
有(a+b)(a²-ab+b²)=a³-a²b+ab²+a²b-ab²+b³=a³+b³即(a+b)(a²-ab+b²)=a³+b³又因为分解因式与整式乘法之间存在互逆关系,所以a³+b³可以分解为(a+b)(a²-ab+b²).请回答下列问题 注:³为立方,²为平1.分解因式 (1)27+x³ (2)125m³+(-n)³ 2猜想a³+b³分解因式结果
根据多项式乘法法则有(a+b)(a²-ab+b²)=a³-a²b+ab²+a²b-ab²+b³=a³+b³即(a+b)(a²-ab+b²)=a³+b³又因为分解因式与整式乘法之间存在互逆关系,所以a³+b&
(1)27+x³
=3³+x³
=3³-3²x+3x²+3²x-3x²+x³
=(3+x)(3²-3x+x²)
=(3+x)(9-3x+x²)
(2)125m³+(-n)³
=(5m)³+(-n)³
=(5m)³-(5m)²×(-n)+5×(-n)²+(5m)²×(-n)+5-5×(-n)²+(-n)³
=(5m+(-n))((5m)²-(5m)×(-n)+(-n)²)
=(5m-n)(25m²+5mn+n²)
(3)a³+b³=(a+b)(a²-ab+b²)