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Factors of Algebraic Expressions

Question 19Fa...

Question

Question 19

Factorised form of $23 x y - 46 x + 54 y - 108$ is
a) $(23 x + 54) (y - 2)$
b) $(23 x + 54 y) (y - 2)$
c) $(23 x y + 54 y) (- 46 x - 108)$
d) $(23 x + 54) (y + 2)$

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Solution

a) $(23 x + 54) (y - 2)$

We have,
$23 x y - 46 x + 54 y - 108 = 23 x y - 2 \times 23 x + 54 y - 2 \times 54 = 23 x (y - 2) + 54 (y - 2)$
$= (y - 2) (23 x + 54)$ [taking (y-2) common]
$= (23 x + 54) (y - 2)$

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