Given:
It is given that the height of the rectangle is [tex]n^3+4n^2+3n[/tex]
The width of the rectangle is [tex]n^3+5n^2[/tex]
We need to determine the area of the entire rectangle.
Area of the rectangle:
The area of the rectangle can be determined using the formula,
[tex]A=height \times width[/tex]
Substituting the values, we have;
[tex]A=(n^3+4n^2+3n)(n^3+5n^2)[/tex]
Multiplying each term within the parenthesis, we get;
[tex]A=n^{3} n^{3}+n^{3} \cdot 5 n^{2}+4 n^{2} n^{3}+4 n^{2} \cdot 5 n^{2}+3 n n^{3}+3 n \cdot 5 n^{2}[/tex]
Simplifying, we get;
[tex]A=n^{6}+5 n^{5}+4n^{5}+20 n^{4}+3 n^{4}+15 n^{3}[/tex]
Adding the like terms, we have;
[tex]A=n^{6}+9n^{5}+23 n^{4}+15 n^{3}[/tex]
Thus, the area of the entire rectangle is [tex]n^{6}+9 n^{5}+23 n^{4}+15 n^{3}[/tex]
