Answer:
[tex]\large\boxed{A=x^2+23x+49}[/tex]
Step-by-step explanation:
Subtract the area of a square (x + 1) × (x + 1)
from the area of a rectangle (x + 10) × (2x + 5)
The area of a square:
[tex]A_s=(x+1)(x+1)[/tex] use FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex]A_s=(x)(x)+(x)(1)+(1)(x)+(1)(1)=x^2+x+x+1=x^2+2x+1[/tex]
The area of a rectangle:
[tex]A_r=(x+10)(2x+5)[/tex] use FOIL
[tex]A_r=(x)(2x)+(x)(5)+(10)(2x)+(10)(5)=2x^2+5x+20x+50=2x^2+25x+50[/tex]
The area of a figure:
[tex]A=A_r-A_s[/tex]
Substitute:
[tex]A=(2x^2+25x+50)-(x^2+2x+1)=2x^2+25x+50-x^2-2x-1[/tex]
combine like terms
[tex]A=(2x^2-x^2)+(25x-2x)+(50-1)=x^2+23x+49[/tex]
