1. Bell Ringers
Combine like terms for the following expressions. Be careful with negatives and be sure to swoosh swoosh when needed.
2n3 - 3n2 + 8 – 8n n
(-5x) + 3x2 + 7x - (-6x2) +12
8t4 – 4t2 + 8t3 – t2 – t4 + 10
(-7y) + 2y – (-3y) – 5y2 +78
10k4 + 3k – 10 + (-8k4 ) + (-2k2 ) + 2k
(-x3) – x – (-3x2) – 25 – (-7x3)
3t2 + 8x (-2t2) – 4x – (4x2) -15
(-10m) + (-2m2) – 14 – (-2m) + 32m2 – (-47t3)

2. Simplifying Expressions: Distributive Property

3. Distributive Property
Do you remember the Opera Property? Well we will be using this property to help us simplify expressions. The Distributive property states you can multiply a sum by multiplying each addend separately and then add the products. 7((-14) + 2) = (7 x (-14)) + (7 x 2)

4. How do we apply this to simplifying expressions?
2(3x +5) When we see this expression we see that we must multiply the expression 3x + 5 by two. Well if we think of this as repeated addition we can see that it is asking us to add the expression 3x + 5 twice 3x x + 5. When we combine our like terms we get 6x + 10.

5. So how does this relate to the distributive property?
2(3x + 5) If we operate this property we see the following equation 2(3x) + 2 x 5: We then can multiply the constants and the variables to combine our like terms more quickly. 2 x 3x = 6x and 2 x 5 = 10 Our new equation is 6x + 10

6. You try
10(5y + 14)

7. What if there are more than two addends?
If there are more than two addends you follow the same procedure. Remember the number outside the parenthesis is the gift Opera is giving and the numbers in the parenthesis is the studio audience, or who is getting the gift. You have to make sure each member of the audience gets a gift. 6(3n + 2n2 + 8)

8. You Try
8(7k2 – 4k + 9)

9. What if there is more than one equation?
7(3y – 5) – 2(10 + (-4y)) First step is to swoosh, swoosh our equations. Remember we do not like subtraction in our equations. Second step is to opera the equations. Combine like terms and rewrite the equation.

10. You try
5((-8y – 5) – 4(8 + (-6y))

11. You Try
2(6y + ( -9)) + 4((-3 + (-8y))

12. Building on
(-9)(10k – 3)

13. Building On
12((-6m2 + 2m – 10)

14. Building On
5((-8y) – 5) – 4(8 + (-6y))

15. Building On
(-3)(6k – 5) + 4((-7) + (-4k))