Answer
$(10x+15) \ \ \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}^{2}$.
Work Step by Step
Find the total area of the outer square.
$(x+4)^{2}$
...square the binomial.
$=x^{2}+2(x)(4)+4^{2}$
...simplify.
$=x^{2}+8x+16$
Find the area of the inner square.
$(x-1)^{2}$
...square the binomial.
$=x^{2}-2(x)(1)+1$
...simplify.
$=x^{2}-2x+1$
Find the area of the figure
Area of figure=(Area of outer square) - (Area of inner square)
$A=x^{2}+8x+16-(x^{2}-2x+1)$
...remove parentheses.
$=x^{2}+8x+16-x^{2}+2x-1$
...group like terms.
$=x^{2}-x^{2}+8x+2x+16-1$
...add like terms.
$=10x+15$
The area of the figure is $(10x+15) \ \ \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}^{2}$.
