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Factorisation by Common Factors

There are 3x+...

Question

There are (3x+5y) shelves in a library and in each shelve there are (5x+3y) the books are there in the liabrary .How many books are there in the library?

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Solution

Number of shelves in the library $= 3 x + 5 y$

Number of books in each shelf $= 5 x + 3 y$

Total number of books in the library $= (3 x + 5 y) (5 x + 3 y)$

$= 3 x (5 x + 3 y) + 5 y (5 x + 3 y)$

$= 15 x^{2} + 9 x y + 15 y^{2} + 25 x y$

$= 15 x^{2} + 34 x y + 15 y^{2}$

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