Evaluate
\left(m+5\right)\left(m+n+8\right)
Expand
m^{2}+mn+13m+5n+40
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m^{2}+10m+25+\left(3+n\right)\left(5+m\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+5\right)^{2}.
m^{2}+10m+25+15+3m+5n+nm
Use the distributive property to multiply 3+n by 5+m.
m^{2}+10m+40+3m+5n+nm
Add 25 and 15 to get 40.
m^{2}+13m+40+5n+nm
Combine 10m and 3m to get 13m.
m^{2}+10m+25+\left(3+n\right)\left(5+m\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+5\right)^{2}.
m^{2}+10m+25+15+3m+5n+nm
Use the distributive property to multiply 3+n by 5+m.
m^{2}+10m+40+3m+5n+nm
Add 25 and 15 to get 40.
m^{2}+13m+40+5n+nm
Combine 10m and 3m to get 13m.
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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