Expand this:- $(3 x + 4 y) (3 x + 5 y)$

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Solution

Solution:-
$(3 x + 4 y) (3 x + 5 y)$
$= [3 x (3 x + 5 y)] + [4 y (3 x + 5 y)]$
$= [3 x (3 x) + 3 x (5 y)] + [4 y (3 x) + 4 y (5 y)]$
$= (9 x^{2} + 15 x y) + (12 x y + 20 y^{2})$
$= 9 x^{2} + 15 x y + 12 x y + 20 y^{2}$
$= 9 x^{2} + 27 x y + 20 y^{2}$
Hence $(3 x + 4 y) (3 x + 5 y) = 9 x^{2} + 27 x y + 20 y^{2}$

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