Question

Write an expression to represent the area of the rectangle below in simplest form. ​

Answer 1

Given:

The length of the rectangle is:

$l=x^2-x+3$

The width of the rectangle is:

$w=4x+1$

To find:

The area of the given rectangle in the simplest form.

Solution:

We know that, the area of a rectangle is:

$A=l\times w$

Where, l is the length and w is the width of the rectangle.

Using the above formula, the area of the given rectangle is:

$A=(x^2-x+3)\times (4x+1)$

$A=x^2(4x)+x^2(1)-x(4x)-x(1)+3(4x)+3(1)$

$A=4x^3+x^2-4x^2-x+12x+3$

$A=4x^3-3x^2+11x+3$

Therefore, the area of the given rectangle is $(4x^3-3x^2+11x+3)$ sq. units.