How do you factor $6 x^{2} - 21$ $6x^2-21$ ?

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How do you factor $6 x^{2} - 21$ $6x^2-21$ ?

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Answer 1 · 2016-09-02T21:30:37

$6 x^{2} - 21 = 3 (\sqrt{2} x - \sqrt{7}) (\sqrt{2} x + \sqrt{7})$ $6x^2-21 = 3(sqrt(2)x-sqrt(7))(sqrt(2)x+sqrt(7))$

Explanation:

The difference of squares identity can be written:

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

We use this with $a = \sqrt{2} x$ $a=sqrt(2)x$ and $b = \sqrt{7}$ $b=sqrt(7)$ as follows:

$6 x^{2} - 21 = 3 (2 x^{2} - 7)$ $6x^2-21 = 3(2x^2-7)$

$6 x^{2} - 21 = 3 ({(\sqrt{2} x)}^{2} - {(\sqrt{7})}^{2})$ $color(white)(6x^2-21) = 3((sqrt(2)x)^2-(sqrt(7))^2)$

$6 x^{2} - 21 = 3 (\sqrt{2} x - \sqrt{7}) (\sqrt{2} x + \sqrt{7})$ $color(white)(6x^2-21) = 3(sqrt(2)x-sqrt(7))(sqrt(2)x+sqrt(7))$

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How do you factor $6 x^{2} - 21$ $6x^2-21$ ?

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