How do you factor $48 x^{2} + 16 x - 16$ $48x^2 + 16x - 16$ ?

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How do you factor $48 x^{2} + 16 x - 16$ $48x^2 + 16x - 16$ ?

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Answer 1 · 2016-09-14T17:52:52

$48 x^{2} + 16 x - 16 = \frac{4}{3} (6 x + 1 - \sqrt{13}) (6 x + 1 + \sqrt{13})$ $48x^2+16x-16 = 4/3(6x+1-sqrt(13))(6x+1+sqrt(13))$

Explanation:

The difference of squares identity can be written:

$a^{2} - b^{2} = (a - b) (a + b)$ $a^2-b^2=(a-b)(a+b)$

Use this with $a = (6 x + 1)$ $a=(6x+1)$ and $b = \sqrt{13}$ $b=sqrt(13)$ as follows:

$48 x^{2} + 16 x - 16 = \frac{4}{3} (36 x^{2} + 12 x - 12)$ $48x^2+16x-16 = 4/3(36x^2+12x-12)$

$48 x^{2} + 16 x - 16 = \frac{4}{3} (36 x^{2} + 12 x + 1 - 13)$ $color(white)(48x^2+16x-16) = 4/3(36x^2+12x+1-13)$

$48 x^{2} + 16 x - 16 = \frac{4}{3} ({(6 x + 1)}^{2} - {(\sqrt{13})}^{2})$ $color(white)(48x^2+16x-16) = 4/3((6x+1)^2-(sqrt(13))^2)$

$48 x^{2} + 16 x - 16 = \frac{4}{3} ((6 x + 1) - \sqrt{13}) ((6 x + 1) + \sqrt{13})$ $color(white)(48x^2+16x-16) = 4/3((6x+1)-sqrt(13))((6x+1)+sqrt(13))$

$48 x^{2} + 16 x - 16 = \frac{4}{3} (6 x + 1 - \sqrt{13}) (6 x + 1 + \sqrt{13})$ $color(white)(48x^2+16x-16) = 4/3(6x+1-sqrt(13))(6x+1+sqrt(13))$

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How do you factor $48 x^{2} + 16 x - 16$ $48x^2 + 16x - 16$ ?

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