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Question

Suppose you are using algebra tiles to represent each expression below. How many unit tiles would you need to add to build a perfect square? a. x2+10xx^{2}+10 x b. x26xx^{2}-6 x c. x2+22xx^{2}+22 x

Solution

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You build a perfect square if the expression is of the form x2±2ax+a2x^2\pm 2ax+a^2:

a. Note that a=5a=5 and thus a2=25a^2=25 is the number of unit tiles.

b. Note that a=3a=3 and thus a2=9a^2=9 is the number of unit tiles.

c. Note that a=11a=11 and thus a2=112=121a^2=11^2=121 is the number of unit tiles.

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