Question

(4m+5n)^²+(5m+4n)^2=?​

Answer 1

$\huge\mathbb{A~N~S~W~E~R}$
$<b>$

$= {(4m + 5n)}^{2} + {(5m + 4n)}^{2} \\ \\ = {16m}^{2} + 40mn + 25 {n}^{2} + 25 {m}^{2} + 40 mn + 16 {n}^{2} \\ \\ = 16 {m}^{2} + 25 {n}^{2} + 25 {m}^{2} + 16 {n}^{2} + 80mn$

${\small\color{Red}{Answer~is~ 16 {m}^{2} + 25 {n}^{2} + 25 {m}^{2} + 16 {n}^{2} + 80mn }}$

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Answer 2

(a+b)2=a2+2ab+b2

(4m+5n)2+(5m+4n)2=16m2+25n2+40mn+25m2+16n2+40mn

=41m2+41n2+80mn