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Factorisation

Factorize the...

Question

Factorize the following expression:

$(2 x + 1)^{2} - 9 x^{4}$

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Solution

Given: $(2 x + 1)^{2} - 9 x^{4}$

$∴ (2 x + 1)^{2} - 9 x^{4}$
$= (2 x + 1)^{2} - (3 x^{2})^{2}$

Using the formula, $(a^{2} - b^{2}) = (a - b) (a + b)$
$= (2 x + 1 + 3 x^{2}) (2 x + 1 - 3 x^{2})$
$= (3 x^{2} + 2 x + 1) (- 3 x^{2} + 2 x + 1)$

Hence, $(2 x + 1)^{2} - 9 x^{4} = (3 x^{2} + 2 x + 1) (- 3 x^{2} + 2 x + 1)$

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