Question

HELP PLEASE SHOW STEPS I HAVE NO IDEA WHAT TO DO. I HAVE BEEN TRYING TO FIGURE IT OUT BUT I CAN’T.

Answer 1

Answer: $x^{2} +23x+49$

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) = $2x^{2} +25x+50$

Then, simplify the smaller rectangle's area:

(x+1)×(x+1) = $x^{2} +2x+1$

Finally, subtract the smaller rectangle's area from the larger rectangle's area:

$(2x^{2} +25x+50) - (x^{2} +2x+1) = x^{2} +23x+49$

Therefore, the final answer is $x^{2} +23x+49$.

I hope this helps!

Answer 2

$\text{Area of rectangle}=\text{lengh}\times\text{width}\\\text{Area of square}=\text{side}^2$

You just need to find differens between rectangle and square

$\text{lengh}\times\text{width}-\text{side}^2\\\\(x+10)(2x+5)-(x+1)^2=2x^2+5x+20x+50-x^2-2x-1=x^2+23x+49$

$x^2+23x+49\:\text{is our answer}$