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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