Geometric Modeling Consider the figure, which is a square divided into two squares and two...

Geometric Modeling Consider the figure, which is a square divided into two squares and two rectangles.

(a) The length of each side of the largest square is x + y. Use the formula for the area of a square to write the area of the largest square as a power.

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(b) Use the formulas for the area of a square and the area of a rectangle to write the area of the largest square as a trinomial that represents the sum of the areas of the four figures that comprise it.

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(c) Explain why the expressions in parts (a) and (b) must be equivalent.

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(d) What special product formula from this section does this exercise reinforce geometrically?