The product of two binomials can be found by multiplying EACH term in one binomial by EACH term in the other binomial Then, simplify (collect like terms)

A BCD Angelina and Brad go to the movies, where they meet Courtney and David.

If they were to all shake hands with the people they are just meeting… who would shake hands with who? A BCD

A BCD A and C A and D B and C B and D

Example 1: Expand and simplify. a) b) In this case, the 2y is multiplied by y and the 2y is multiplied by 1. In this case, the 3 ‘meets’ the x and the 3 ‘meets’ the 2.

c) d)

e)

When factoring polynomial expressions, look at both the numerical coefficients and the variables to find the greatest common factor (G.C.F.) Look for the greatest common numerical factor and the variable with the highest degree of the variable common to each term To check that you have factored correctly, EXPAND your answer (because EXPANDING is the opposite of FACTORING!)

Example 2: Factor. a) b) c)

In multiplication questions, the terms that are multiplied together are called factors Example: 12 = 6 x 2  6 and 2 are factors of = 4 x 3  4 and 3 are also factors of 12 A repeated multiplication of equal factors (the same number) can b expressed as a power Example: 3 x 3 x 3 x 3 = 3 4  3 4 is the power  3 is the base  4 is the exponent

Examples 6 3 = 6 x 6 x = (5 x 5) + (3 x 3) = 36 x 6 = = 216 = 34

The Power of Negative Numbers There is a difference between –3 2 and (–3) 2 The exponent affects ONLY the number it touches So, –3 2 = –(3 x 3), but (–3) 2 = (–3) x (–3) = –9 = 9

Exponent Laws: Any exponent raised to the exponent zero is equal to one Ex. 2 0 = = = 1 …. Why is this? Think, pair, share. Turn to your partners and brainstorm about this for 2 minutes. Hint: Think about the quotient rule…