Factor the expression completely 18x^4 - 12x^2

Answer 1

To factor the expression \( 18x^4 - 12x^2 \) completely, we can follow these steps:

1. Identify the Greatest Common Factor (GCF):

   • The coefficients \( 18 \) and \( 12 \) have a GCF of \( 6 \).
   • The variable terms \( x^4 \) and \( x^2 \) have a GCF of \( x^2 \).

   Therefore, the GCF of the entire expression is \( 6x^2 \).

2. Factor out the GCF: \[ 18x^4 - 12x^2 = 6x^2(3x^2 - 2) \]

3. Check if the remaining expression can be factored:

   • The expression \( 3x^2 - 2 \) is a difference of terms, but it does not factor nicely over the integers or rationals as it is irreducible.

Thus, the completely factored form of the expression \( 18x^4 - 12x^2 \) is:

\[ \boxed{6x^2(3x^2 - 2)} \]