SOLUTION: 1. Use algebra to explain why the middle term 2ab is needed in the expression (a+b)^2=a^2+2ab+b^2 2. Use geometry to explain why the term 2ab is needed. Specifically, notice th

Question 776933: 1. Use algebra to explain why the middle term 2ab is needed in the expression (a+b)^2=a^2+2ab+b^2
2. Use geometry to explain why the term 2ab is needed. Specifically, notice that the area of a square side a+b is (a+b)^2. On the other hand, this area is the sum of areas of both sqaures, plus the areas of the two retangles.
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
#2 is more fun.

Draw a segment and label length a. EXTEND the segment and label the extended part length b. Draw a square using this combined segment of a+b. LABEL the lengths a and b on each side of the square. The lengths a and b at right angles to the lengths from these two neighboring sides of this square form FOUR regions. You can represent the expressions for the areas of each of these four regions. You find there is a region of area ab and it occurs in this figure TWO times.
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