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Page 1 of 2 ACTIVITY 5.5 Developing Concepts Using Algebra Tiles to Complete the Square QUESTION Given b, what is the value of c that makes x 2 + bx + c EXPLORING THE CONCEPT GROUP ACTIVITY Work with a partner. MATERIALS algebra tiles Group Activity for use with Lesson 5.5 a perfect square trinomial? 1 Use algebra tiles to model the expression x2 + 6x. You will need one x 2-tile and six x-tiles. 2 Arrange the tiles in a square. Your arrangement will be incomplete in one corner. You want the length and width of your “square” to be equal. 3 Determine the number of 1-tiles needed to complete the square. By adding nine 1-tiles, you can see that x 2 + 6x + 9 = (x + 3)2. Square Completing the en Expression writt Number of 1-tiles e re et ua pl sq m a co as to ed ed ne Expression the square ? ? 2 2x ? x ? ? 2 ? x 2 4x 2 6x 9 (x 3) x 9 ? x 2 6x ? ? ? x 2 8x ? ? ? 2 10x x DRAWING CONCLUSIONS 1. Copy and complete the table at the left by following the steps above. 2. Look for patterns in the last column of your table. Consider the general statement x2 + bx + c = (x + d)2. a. How is d related to b in each case? b. How is c related to d in each case? c. How can you obtain the numbers in the second column of the table directly from the coefficients of x in the expressions from the first column? 5.5 Concept Activity 281