How do you factor $f (x) = x^{4} - 9 x^{2}$ $f(x)= x^4 - 9x^2$ ?

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How do you factor $f (x) = x^{4} - 9 x^{2}$ $f(x)= x^4 - 9x^2$ ?

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Answer 1 · 2018-05-15T12:56:19

$= x^{2} \cdot (x - 3) (x + 3)$ $=x^2*(x-3)(x+3)$

Explanation:

$x^{4} - 9 x^{2}$ $x^4 - 9x^2$

take $x^{2}$ $x^2$ as a common factor:

$x^{2} \cdot (x^{2} - 9)$ $color(red)(x^2)*(x^2-9)$

now what is inside the parentheses we can factor them by the difference between two squares formula: $x^{2} - 9 = x^{2} - 3^{2}$ $color(blue)(x^2-9=x^2-3^2)$

now difference between two squares formula

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

$x^{2} - 3^{2} = (x - 3) (x + 3)$ $color(blue)(x^2-3^2 = (x-3)(x+3))$

$= x^{2} \cdot (x - 3) (x + 3)$ $=color(red)(x^2)*color(blue)((x-3)(x+3))$

$= x^{2} \cdot (x - 3) (x + 3)$ $=x^2*(x-3)(x+3)$

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How do you factor $f (x) = x^{4} - 9 x^{2}$ $f(x)= x^4 - 9x^2$ ?

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