Mathematics: Find an algebraic expression that represents the area of the shaded region

Find an algebraic expression that represents the

Ответ:

Geo777

07.01.2022

taking a peek at the outer rectangle, it has a length of 4x - 3 and a width of "x", so it has an area of (4x-3)(x).

now, the tiny square inside the larger rectangle, has an area of (x-4)(x-4), if we subtract the area of the square inside from the area of the larger rectangle, what's leftover is just the shaded area.

$\bf \stackrel{\textit{area of rectangle}}{(4x-3)(x)}~~-~~\stackrel{\textit{area of the square}}{(x-4)(x-4)}\implies 4x^2-3x~~~~-~~~~\stackrel{F~O~I~L}{(x^2-8x+16)} \\\\\\ 4x^2-3x~~~~-~~x^2+8x-16\implies 3x^2+5x-16$