Adi used algebra tiles to represent the product (negative 2 x minus 1)(2 x minus 1). an algebra tile configuration. 4 tiles are in the factor 1 spot: 2 are labeled negative x and 2 are labeled negative. 3 tiles are in the factor 2 spot: 2 are labeled + x and 1 is labeled negative. 12 tiles are in the product spot: 4 are labeled negative x squared, 4 are labeled negative x, 2 are labeled + x, and 2 are labeled +. which is true regarding adi’s use of algebra tiles? she used the algebra tiles correctly. she did not represent the two original factors correctly on the headers. the signs on some of the products are incorrect. some of the products do not show the correct powers of x.

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.