Answer: [tex]x^{2} +23x+49[/tex]
Step-by-step explanation:
To find the area of the shaded region, you must find the area of the larger rectangle [(x+10)×(2x+5)] and subtract the area of the smaller rectangle [(x+1)×(x+1)] from it.
First, you simplify the larger rectangle's area:
(x+10)×(2x+5) = [tex]2x^{2} +25x+50[/tex]
Then, simplify the smaller rectangle's area:
(x+1)×(x+1) = [tex]x^{2} +2x+1[/tex]
Finally, subtract the smaller rectangle's area from the larger rectangle's area:
[tex](2x^{2} +25x+50) - (x^{2} +2x+1) = x^{2} +23x+49[/tex]
Therefore, the final answer is [tex]x^{2} +23x+49[/tex].
I hope this helps!
