This document discusses techniques for multiplying polynomials including squaring binomial expressions, FOIL method, and multiplying conjugates. When squaring a binomial expression (x + a)2, the result is x2 + 2ax + a2. Multiplying conjugates, which are similar expressions with opposite operations like (x - a)(x + a), will result in the middle terms cancelling out when combined.

1. Multiplying polynomials

2. FOIL

3. Double distributive Image from Prentice Hall Mathematics NC Algebra I 2004

4. Squaring When you square anything, it means to multiply it by itself... even if it's a binomial. So if you have (x + 3)2 it's saying to multiply (x + 3)(x + 3). When you do this, you will get x2 + 3x + 3x + 9...or x2 + 6x + 9. Notice the middle term's coefficient is 2*3 and the last number is 3*3. This pattern will always occurring when you are squaring. So if you have (x + 5)2 the result would be x2 + 10x + 25 after you combine like terms. If you have binomial that used subtraction, like (x - 4)2, you would multiply (x - 4)(x - 4). The pattern would be similar except the middle term would now be negative. So your solution would be x2 - 8x + 16.

5. What is a conjugate? A conjugate is when you have two expressions that look exactly the same, but are opposite operations. An example would be ( x - 6) and (x + 6). When you multiply conjugates, when you combine like terms, they will add to zero. If we multiplied the two expressions (x -6)(x + 6), you would have x2 - 6x + 6x - 36...or just x2 - 36.