Now consider the expression x2 + 6x + 7. The pieces of this
expression can be represented with an "x by x" square, six "x by 1"
rectangles, and seven unit squares.
x2 + 6x + 7
a. Why is it impossible to arrange the given squares and rectangles
without overlapping to form one large square?
b. How could you produce the requested square if you were given
some extra pieces or allowed to take away some pieces? What
addition or subtraction would do the job most efficiently?
c. Explain how your answer to Part b illustrates the fact that
x2 + 6x + 7 = (x + 3)2 – 2.
