How do you factor the expression #27x^2-3#?

2 Answers
Jim G.
Apr 13, 2018

#3(3x-1)(3x+1)#

Explanation:

#"take out a "color(blue)"common factor "3#

#=3(9x^2-1)#

#9x^2-1" is a "color(blue)"difference of squares"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#"here "9x^2=(3x)^2rArra=3x" and "b=1#

#rArr9x^2-1=(3x-1)(3x+1)#

#rArr27x^2-1=3(3x-1)(3x+1)#

Watchmojo J.
Apr 13, 2018

#3(3x-1)(3x+1)#

Explanation:

#27x^2-3#

#=3(9x^2-1)#

Differences of two squares rule:

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

Because:
#(a+b)(a-b) = a^2+ba-ab-b^2 = a^2-b^2#

#a^2# can be replaced with #9x^2#

#b^2# can be replaced with #1#

#=3(sqrt(9x^2) + sqrt(1))(sqrt(9x^2) - sqrt(1))#

#=color(red)(3(3x-1)(3x+1)#

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