Answer
a) $x^2+8x$
b) $16$
c) $x^2+8x=16$
d) $(x+4)^2$
Work Step by Step
a) The small square has side $x$, while the rectangles have length $x$ and width $1$, so the binomial in $x$ representing the combined area of the small square and the $8$ rectangles is:
$$x^2+8(x)(1)=x^2+8x.$$
b) The area completing the big square contains $16$ squares of side $1$:
$$16(1^2)=16.$$
c) The trinomial representing the area of the big (complete) square is:
$$x^2+8x+16.$$
d) Rewrite the area of the complete square using its side $x+4$:
$$(x+4)^2.$$
