How do you simplify $9 x^{2} - 5 x^{4}$ $9x^2-5x^4$ ?

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How do you simplify $9 x^{2} - 5 x^{4}$ $9x^2-5x^4$ ?

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Answer 1 · 2015-09-28T10:55:57

$9 x^{2} - 5 x^{4} = x^{2} (3 - \sqrt{5} x) (3 + \sqrt{5} x)$ $9x^2-5x^4 = x^2(3-sqrt(5)x)(3+sqrt(5)x)$

Explanation:

$9 x^{2} - 5 x^{2}$ $9x^2-5x^2$

$XXX$ $color(white)("XXX")$ extracting the obvious factor of $x^{2}$ $x^2$
$= x^{2} (9 - 5 x^{2})$ $=x^2(9-5x^2)$

$XXX$ $color(white)("XXX")$ remember that $(a^{2} - b^{2}) = (a - b) (a + b)$ $(a^2-b^2) = (a-b)(a+b)$
$XXX$ $color(white)("XXX")$ and substituting $9 = 3^{2}$ $9 = 3^2$ for $a^{2}$ $a^2$
$XXX$ $color(white)("XXX")$ and $5 x^{2} = {(\sqrt{5} x)}^{2}$ $5x^2 = (sqrt(5)x)^2$ for $b^{2}$ $b^2$
$= x^{2} (3 - \sqrt{5} x) (3 + \sqrt{5} x)$ $=x^2(3-sqrt(5)x)(3+sqrt(5)x)$

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How do you simplify $9 x^{2} - 5 x^{4}$ $9x^2-5x^4$ ?

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