SOLUTION: Use algebra to explain why the middle term 2ab is needed in the expression (a + b)� = a� + 2ab + b�. Use geometry to explain why the term 2ab is needed. Specifically, notice that

Question 829497: Use algebra to explain why the middle term 2ab is needed in the expression (a + b)� = a� + 2ab + b�.
Use geometry to explain why the term 2ab is needed. Specifically, notice that the area of a square with side a + b is (a + b)�. On the other hand, this area is the sum of areas of both squares, plus the areas of the two rectangles

Answer by josgarithmetic(39628) (Show Source): You can put this solution on YOUR website!
Exactly as you described. You can represent a square composed of sides, a+b. The lengths a and b can each be projected at right angles from each of this square's sides. In this projective action, a and b from each side will sweep into these four areas:
a*a, b*b, and TWO of a*b.

The a*b may be a rectangle. The a*a and b*b are both squares.

All that is very easy to draw and label. Seeing and understanding is also easier that way.

If you will do all that, you will also see why the Distributive Property of "Algebra 1, 2, and 3" work.
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