Question

multiple choice 1 point what is the gcf of the terms: 12x²y and 18xy? 6x²y 6xy 12xy 3x²y²

Explanation:

Step1: Factor coefficients

Prime factors: $12=2^2\times3$, $18=2\times3^2$
GCF of coefficients: $\gcd(12,18)=6$

Step2: Factor $x$-terms

$x^2$ and $x^1$
GCF of $x$-terms: $x^{\min(2,1)}=x$

Step3: Factor $y$-terms

$y^1$ and $y^2$
GCF of $y$-terms: $y^{\min(1,2)}=y$

Step4: Combine all GCFs

Multiply coefficient, $x$-term, $y$-term GCFs

Answer:

$\boldsymbol{6xy}$ (Option: $\boldsymbol{6xy}$)