Question

which of the following expressions is equivalent to $18x^4 - 12x^2$?
$6\left(3x^2 - 2x^2\
ight)$
$6x\left(2x^3 - 2x\
ight)$
$x^2\left(18x^2 - 12\
ight)$
$6x^2\left(3x^2 - 2\
ight)$

Explanation:

Step1: Identify GCF of terms

Find GCF of $18x^4$ and $12x^2$:
GCF of coefficients: $\gcd(18,12)=6$
GCF of variables: $\gcd(x^4,x^2)=x^2$
Overall GCF: $6x^2$

Step2: Factor out the GCF

Divide each term by $6x^2$:
$\frac{18x^4}{6x^2}=3x^2$, $\frac{-12x^2}{6x^2}=-2$
Factored form: $6x^2(3x^2 - 2)$

Step3: Verify other options

• Green: $6(3x^2-2x^2)=6x^2

eq 18x^4-12x^2$

• Purple: $6x(2x^3-2x)=12x^4-12x^2

eq 18x^4-12x^2$

• Orange: $x^2(18x^2-12)=18x^4-12x^2$ (not fully factored, but the question asks for equivalent; however, the fully factored option is the correct equivalent match here)

Answer:

D. $6x^2 (3x^2 - 2)$