Let's simplify each expression and determine the degree of the resulting polynomial.

1. $6(2 - 3)$ $6 \times (-1) = -6$

   • This is a constant, so the degree is 0.

2. $5(x + 2x)$ $5(3x) = 15x$

   • The highest power of $x$ is 1, so the degree is 1.

3. $4x(x + 2)$ $4x^2 + 8x$

   • The highest power of $x$ is 2, so the degree is 2.

4. $5(2x - 4)$ $10x - 20$

   • The highest power of $x$ is 1, so the degree is 1.

5. $(x + 4)(x + 6)$ $x^2 + 6x + 4x + 24 = x^2 + 10x + 24$

   • The highest power of $x$ is 2, so the degree is 2.

6. $(x + 3)(x - 2)$ $x^2 - 2x + 3x - 6 = x^2 + x - 6$

   • The highest power of $x$ is 2, so the degree is 2.

Summary:

Expression	Simplified Form	Degree
$6(2 - 3)$	$-6$	0
$5(x + 2x)$	$15x$	1
$4x(x + 2)$	$4x^2 + 8x$	2
$5(2x - 4)$	$10x - 20$	1
$(x + 4)(x + 6)$	$x^2 + 10x + 24$	2
$(x + 3)(x - 2)$	$x^2 + x - 6$	2

Would you like me to provide step-by-step explanations for any of these?

Related Questions:

1. What is the degree of a polynomial, and how is it determined?
2. How do you expand binomials using the distributive property?
3. What are some real-world applications of polynomials?
4. How do you factor quadratic expressions?
5. Can a polynomial have a negative degree?

Tip: The degree of a polynomial is the highest exponent of the variable in its simplified form.