(5m^2+3n^2)^2-(3m^2+5n^2)^2因式分解
来源:百度知道 编辑:UC知道 时间:2024/05/21 22:34:26
(5m^2+3n^2)^2-(3m^2+5n^2)^2因式分解
小茴来为你解答,原式=2(5m²+3n²-3m²-5n²)
=2(2m²-2n²)
=4m²-4n²
=(2m+2n)(2m-2n)
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利用平方差公式。
原式=[(5m^2+3n^2)+(3m^2+5n^2)][(5m^2+3n^2)-(3m^2+5n^2)]
=(8m^2+8n^2)(2m^2-2n^2)
=16(m^2+n^2)(m^2-n^2)
=16(m^2+n^2)(m+n)(m-n)
(m-n)2(n-m)3(n-m)4
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