How do you factor the expression $4 x^{2} - 1$ $4x^2-1$ ?

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How do you factor the expression $4 x^{2} - 1$ $4x^2-1$ ?

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Answer 1 · 2015-12-19T12:34:28

Apply the difference of squares formula to find that
$4 x^{2} - 1 = (2 x + 1) (2 x - 1)$ $4x^2-1 = (2x+1)(2x-1)$

Explanation:

The difference of squares formula states that
$a^{2} - b^{2} = (a + b) (a - b)$ $a^2 - b^2 = (a+b)(a-b)$
(Verify this by expanding the right hand side)

Applying this to the given problem, we have

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

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How do you factor the expression $4 x^{2} - 1$ $4x^2-1$ ?

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