Answer:
The area of the shaded region is [tex]\boldsymbol{x^2+12x+20} \ \textbf{ square units}[/tex]========================================================
Explanation:
For now, let's ignore the 4 by 4 smaller square.
The orange larger square has area of...
[tex](x+6)^2\\\\(x+6)(x+6)\\\\x(x+6)+6(x+6)\\\\x^2+6x+6x+36\\\\x^2+12x+36\\\\[/tex]
You can use the FOIL rule to get the same result. The box method is also a visual handy tool.
No matter which method you use, the area of the orange square is [tex]x^2+12x+36[/tex] if we ignore the 4 by 4 portion.
However, we do have that white portion to take away from the orange square. So we'll subtract off 4*4 = 16 square units to end up with [tex]x^2+12x+36-16 = \boldsymbol{x^2+12x+20}\\\\[/tex]
The orange shaded region has area of [tex]\boldsymbol{x^2+12x+20}[/tex]
If we knew what the value of x was, then we could find an actual numeric result rather than a polynomial like this.
