Factorize each of the following expressions:

$125 x^{2} - 45 y^{2}$

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Solution

Given: $125 x^{2} - 45 y^{2}$

$∴ 125 x^{2} - 45 y^{2}$
$= 5 [25 x^{2} - 9 y^{2}]$
$= 5 [(5 x)^{2} - (3 y)^{2}]$
$= 5 (5 x + 3 y) (5 x - 3 y)$
$[∵ a^{2} - b^{2} = (a + b) (a - b)]$

Hence, $125 x^{2} - 45 y^{2} = 5 (5 x + 3 y) (5 x - 3 y)$ .

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