Factorise completely and state whether the answer is True or False.
$625 - x^{4}$ is $(25 + x^{2}) (5 + x) (5 - x)$

True

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False

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Solution

The correct option is A True
$625 - x^{4} = 25^{2} - {(x^{2})}^{2}$
Formula $a^{2} - b^{2} = (a + b) (a - b)$

Hence, $625 - x^{4} = 25^{2} - {(x^{2})}^{2} = (25 + x^{2}) (25 - x^{2}) = (25 + x^{2}) (5^{2} - x^{2})$
Applying the formula of $a^{2} - b^{2} = (a + b) (a - b)$ again,
$625 - x^{4} = (25 + x^{2}) (5 + x) (5 - x)$

Suggest Corrections

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x^{4} = 16

x = 2

Factorise Completely : $625 - x^{4}$

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