Answer
$2r^{2}-5r-12$
Work Step by Step
The area of a rectangle is:
$A=L \times W $
Given that L = 2r+3 and W= r-4
We substitute it into the equation for area
A = (2r+3)(r-4)
We distribute the first bracket and multiply it with the second bracket.
A= 2r(r-4)+3(r-4)
To simplify the polynomial we apply the distributive property that states:
a(b+c)=ab+ac
A= $(2r \times r)+(2r \times -4)+(3 \times r) + (3 \times -4)$
A= $2r^{2}-8r+3r-12$
A= $2r^{2}-5r-12$
We add like terms to get final answer
