Answer:
Area = 14x + 21 square units
Step-by-step explanation:
The formula of an area of a square with side length a:
[tex]A=a^2[/tex]
The big square:
[tex]a=x+5[/tex]
Substitute:
[tex]A_B=(x+5)^2[/tex] use [tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex]A_B=x^2+2(x)(5)+5^2=x^2+10x+25[/tex]
The small square:
[tex]a=x-2[/tex]
Substitute:
[tex]A_S=(x-2)^2[/tex] use [tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex]A_S=x^2-2(x)(2)+2^2=x^2-4x+4[/tex]
The area of a shaded region:
[tex]A=A_B-A_S[/tex]
Substitute:
[tex]A=(x^2+10x+25)-(x^2-4x+4)=x^2+10x+25-x^2+4x-4[/tex]
combine like terms
[tex]A=(x^2-x^2)+(10x+4x)+(25-4)=14x+21[/tex]
