Question

a rectangle has a height of n3+4n2+3n and a width of n^3+5n^2 express the area of the entire rectangle

Answer 1

Given:

It is given that the height of the rectangle is $n^3+4n^2+3n$

The width of the rectangle is $n^3+5n^2$

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,

$A=height \times width$

Substituting the values, we have;

$A=(n^3+4n^2+3n)(n^3+5n^2)$

Multiplying each term within the parenthesis, we get;

$A=n^{3} n^{3}+n^{3} \cdot 5 n^{2}+4 n^{2} n^{3}+4 n^{2} \cdot 5 n^{2}+3 n n^{3}+3 n \cdot 5 n^{2}$

Simplifying, we get;

$A=n^{6}+5 n^{5}+4n^{5}+20 n^{4}+3 n^{4}+15 n^{3}$

Adding the like terms, we have;

$A=n^{6}+9n^{5}+23 n^{4}+15 n^{3}$

Thus, the area of the entire rectangle is $n^{6}+9 n^{5}+23 n^{4}+15 n^{3}$