因式分解:9(m+n)² -16(m-n)²
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因式分解:9(m+n)² -16(m-n)²
因式分解:9(m+n)² -16(m-n)²
因式分解:9(m+n)² -16(m-n)²
9(m+n)²-16(m-n)²
=[3(m+n)]²-[4(m-n)]²
=[3(m+n)+4(m-n)][3(m+n)-4(m-n)]
=(3m+3n+4m-4n)(3m+3n-4m+4n)
=(7m-n)(7n-m)
这里主要考察平方差公式:a²-b²=(a+b)(a-b)
9(m+n)² -16(m-n)²
=(3m+3n)²-(4m-4n)²
=(3m+3n+4m-4n)(3m+3n-4m+4n)
=(7m-n)(-m+7n)
9(m+n)² -16(m-n)²
=(3m+3n-4m+4n)(3m+3n+4m-4n)
=(-m+7n)(7m-n)
[3(m+n)+4(m-n)]{3(m+n)-4(m-n)}
9(m+n)^2-16(m-n)^2=[3(m+n)-4(m-n)][(3(m+n)+4(m-n)].
=(-m+n)(7m-n).