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

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Solution

$(4 m + 5 n)^{2} + (5 m + 4 n)^{2}$
$= (4 m)^{2} + 2 \times 4 m \times 5 n + (5 n)^{2} + (5 m)^{2} + 2 \times 5 m \times 4 n + (4 n)^{2}$
$[U s i n g i d e n t i t y (a + b)^{2} = a^{2} + 2 a b + b^{2}]$ $= 16 m^{2} + 40 m n + 25 n^{2} + 25 m^{2} + 40 m n + 16 n^{2}$ $= 16 m^{2} + 25 m^{2} + 40 m n + 40 m n + 25 n^{2} + 16 n^{2}$
$= 41 m^{2} + 80 m n + 41 n^{2}$

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

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