Question

(4m+5n)²+(5m+4n)²

answer with explanation
don't scam
if you answer correct with explanation I will mark you as brainlist
​

Answer 1

Answer:

$41 {m}^{2} + 41 {n}^{2} + 80mn$

Step-by-step explanation:

$( {4m + 5n)}^{2} + {(5m + 4n)}^{2} \\ = {(4m)}^{2} + {(5n)}^{2} + 2 \times 4m \times 5n + \\ {(5m)}^{2} + { {(4n)}^{2} } + 2 \times 5m \times 4n \\ = 16 {m}^{2} + 25 {n}^{2} + 40mn \\ + 25 {m}^{2} + 16 {n}^{2} + 40mn \\ = 41 {m}^{2} + 41 {n}^{2} + 80mn$