To find the volume of the rectangular shaped glass, we need to use the formula for the volume of a rectangular prism, which is given by:
[tex]\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\][/tex]
Given:
- Length [tex]\((L)\)[/tex] = [tex]\(4x + 3y\)[/tex]
- Width [tex]\((W)\)[/tex] = [tex]\(2x - y\)[/tex]
- Height [tex]\((H)\)[/tex] = 5
The volume [tex]\(V\)[/tex] can be calculated by substituting these values into the formula:
[tex]\[
V = (4x + 3y) \times (2x - y) \times 5
\][/tex]
First, let's multiply the length and width expressions:
[tex]\[
(4x + 3y)(2x - y)
\][/tex]
To expand this, we use the distributive property (FOIL method):
[tex]\[
= 4x \cdot 2x + 4x \cdot (-y) + 3y \cdot 2x + 3y \cdot (-y)
\][/tex]
[tex]\[
= 8x^2 - 4xy + 6xy - 3y^2
\][/tex]
Combine like terms:
[tex]\[
= 8x^2 + 2xy - 3y^2
\][/tex]
Next, we multiply this result by the height:
[tex]\[
V = (8x^2 + 2xy - 3y^2) \times 5
\][/tex]
Distribute the 5:
[tex]\[
V = 5 \cdot 8x^2 + 5 \cdot 2xy - 5 \cdot 3y^2
\][/tex]
Simplify each term:
[tex]\[
V = 40x^2 + 10xy - 15y^2
\][/tex]
Therefore, the polynomial expression that represents the volume of each glass is:
[tex]\[
\boxed{40x^2 + 10xy - 15y^2}
\][/tex]
