How do you factor #f(x)= x^4 - 9x^2#?

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Answer 1 · 2018-05-15T12:56:19

#=x^2*(x-3)(x+3)#

#x^4 - 9x^2 #

take #x^2# as a common factor:

#color(red)(x^2)*(x^2-9)#

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

now difference between two squares formula

#a^2 - b^2 = (a-b)(a+b)#

#color(blue)(x^2-3^2 = (x-3)(x+3))#

#=color(red)(x^2)*color(blue)((x-3)(x+3))#

#=x^2*(x-3)(x+3)#