因式分解mn(x^2+y^2)+xy(m^2+n^2)

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因式分解mn(x^2+y^2)+xy(m^2+n^2)

因式分解mn(x^2+y^2)+xy(m^2+n^2)
因式分解mn(x^2+y^2)+xy(m^2+n^2)

因式分解mn(x^2+y^2)+xy(m^2+n^2)
mn(x^2+y^2)+xy(m^2+n^2)
=mnx²+mny²+xym²+xyn²
=(mnx²+xym²)+(mny²+xyn²)
=xm(nx+my)+ny(nx+my)
=(nx+my)(xm+ny)

mn( x" + y" ) + xy( m" + n" )
= mnx" + mny" + m"xy + n"xy
= mnx" + m"xy + mny" + n"xy
= mx( nx + my ) + ny( my + nx )
= ( nx + my )( mx + ny )