Question

Simplify:
$(4m+5n{)}^2+(5m+4n{)}^2$

Answer 1

$(4m+5n{)}^2+(5m+4n{)}^2$

$=(4m{)}^2+(2\times 4m\times 5n)+(5n{)}^2+(5m{)}^2+(2\times 5m\times 4n)+(4n{)}^2$
$[\text{Using identity},(a+b{)}^2=a^2+2ab+b^2]$

$=16m^2+40mn+25n^2+25m^2+40mn+16n^2$

$=16m^2+25m^2+40mn+40mn+25n^2+16n^2$

$=41m^2+80mn+41n^2$