Factorize the following :

$i .) 25 x^{2} - 36$

$i i .) 36 x^{2} + 49 + 8 x$

$i i i .) 9 + 25 x^{2} - 30 x$ [3 MARKS]

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Solution

Factorisation: 1 Mark each

$i .) 25 x^{2} - 36$
$U s i n g t h e i d e n t i t y a^{2} - b^{2} = (a + b) (a - b)$

$25 x^{2} - 36 = ((5 x)^{2} - 6^{2}) = (5 x + 6) (5 x - 6)$

$i i .) 36 x^{2} + 49 + 84 x$

$= (6 x)^{2} + 7^{2} + 2 (6 x) (7)$

$U s i n g t h e i d e n t i t y a^{2} + 2 a b + b^{2}$ = $(a + b)^{2}$

$= (6 x + 7)^{2}$

$i i i .) 9 + 25 x^{2} - 30 x$

$= 3^{2} + (5 x)^{2} - 2 (5 x) (3)$

$U s i n g t h e i d e n t i t y a^{2} - 2 a b + b^{2}$ = $(a - b)^{2}$

$= (3 - 5 x)^{2}$

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