Factorise the following: $9 x^{2} + 6 x + 1 - 25 y^{2}$
Factorise the following: $a^{2} + b^{2} + 2 a b 2 b c + 2 c a$

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Solution

Part $(1)$

$9 x^{2} + 6 x + 1 - 25 y^{2}$

$= {(3 x)}^{2} + 2 \times 3 x \times 1 + {(1)}^{2} - {(5 y)}^{2}$

$= {(3 x + 1)}^{2} - {(5 y)}^{2} ∴ (a^{2} - b^{2} = (a + b) (a - b))$

$= (3 x + 1 + 5 y) (3 x + 1 - 5 y)$

Hence, this is the answer

Part $(2)$

$a^{2} + b^{2} + 2 a b$

$= a^{2} + a b + a b + b^{2}$

$= a (a + b) + b (a + b)$

$= (a + b) (a + b)$

And

$2 b c + 2 c a$

$= 2 c (b + a)$

$= 2 c (a + b)$

Hence, this is the answer.

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