Question

what is the greatest common factor of $20x^{6}y + 40x^{4}y^{2}-10x^{5}y^{5}$?
$\circ$ $5x^{2}y^{5}$
$\circ$ $5x^{4}y$
$\circ$ $20x^{6}y$
$\circ$ $10x^{4}y$

Explanation:

Step1: Find GCF of coefficients

The coefficients are 20, 40, and 10.
$\gcd(20,40,10) = 10$

Step2: Find GCF of $x$-terms

The $x$-exponents are 6, 4, and 5. The smallest exponent is 4.
$\text{GCF of } x^6, x^4, x^5 = x^4$

Step3: Find GCF of $y$-terms

The $y$-exponents are 1, 2, and 5. The smallest exponent is 1.
$\text{GCF of } y^1, y^2, y^5 = y^1 = y$

Step4: Combine all GCFs

Multiply the GCFs from steps 1-3.
$10 \times x^4 \times y = 10x^4y$

Answer:

10$x^4y$ (corresponding to the option: $10x^4y$)