$Factorise: 25 + 70 x + 49 x^{2}$

$(5 x + 7) (5 x + 2)$

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$(7 x + 5) (5 x + 3)$

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$(7 x + 5) (7 x + 5)$

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$(3 x + 7)^{2}$

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Solution

The correct option is C
$(7 x + 5) (7 x + 5)$

$Given, the expression is 25 + 70 x + 49 x^{2} .$

The given expression can be rewritten as,
$49 x^{2} + 70 x + 25$

$Using the identity: (a + b)^{2} = a^{2} + 2 a b + b^{2}, we get$

$49 x^{2} + 70 x + 25 = (7 x)^{2} + 2 (5) (7 x) + 5^{2}$
$= (7 x + 5)^{2}$
$= (7 x + 5) (7 x + 5)$

$∴ 25 + 70 x + 49 x^{2} = (7 x + 5) (7 x + 5)$

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