Evaluate
\left(m-n\right)\left(m+4n\right)
Expand
m^{2}+3mn-4n^{2}
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m^{2}-n^{2}+3n\left(m-n\right)
Consider \left(m+n\right)\left(m-n\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
m^{2}-n^{2}+3nm-3n^{2}
Use the distributive property to multiply 3n by m-n.
m^{2}-4n^{2}+3nm
Combine -n^{2} and -3n^{2} to get -4n^{2}.
m^{2}-n^{2}+3n\left(m-n\right)
Consider \left(m+n\right)\left(m-n\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
m^{2}-n^{2}+3nm-3n^{2}
Use the distributive property to multiply 3n by m-n.
m^{2}-4n^{2}+3nm
Combine -n^{2} and -3n^{2} to get -4n^{2}.
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