Let's multiply the polynomial [tex]\( 2x(x - 3y)(2x - y) \)[/tex].
### Step-by-Step Solution
1. Distribute the terms inside the parentheses:
Start by multiplying the first two factors: [tex]\( x \)[/tex] and [tex]\( (x - 3y) \)[/tex].
[tex]\[
x \cdot (x - 3y) = x^2 - 3xy
\][/tex]
2. Multiply the resulting expression by the third factor [tex]\( (2x - y) \)[/tex]:
[tex]\[
(x^2 - 3xy) \cdot (2x - y)
\][/tex]
3. Distribute [tex]\( (2x - y) \)[/tex] to each term inside the parenthesis [tex]\( x^2 - 3xy \)[/tex]:
[tex]\[
x^2 \cdot (2x - y) - 3xy \cdot (2x - y)
\][/tex]
4. Expand the individual products:
[tex]\[
x^2 \cdot 2x = 2x^3
\][/tex]
[tex]\[
x^2 \cdot (-y) = -x^2y
\][/tex]
[tex]\[
-3xy \cdot 2x = -6x^2y
\][/tex]
[tex]\[
-3xy \cdot (-y) = 3xy^2
\][/tex]
5. Combine all the expanded terms:
[tex]\[
2x^3 - x^2y - 6x^2y + 3xy^2
\][/tex]
6. Combine like terms:
[tex]\[
2x^3 - (x^2y + 6x^2y) + 3xy^2 = 2x^3 - 7x^2y + 3xy^2
\][/tex]
7. Finally, multiply everything by 2:
[tex]\[
2 \cdot (2x^3 - 7x^2y + 3xy^2) = 4x^3 - 14x^2y + 6xy^2
\][/tex]
So, the expanded form of the polynomial [tex]\( 2x(x - 3y)(2x - y) \)[/tex] in descending order is:
[tex]\[
\boxed{4x^3 - 14x^2y + 6xy^2}
\][/tex]
