Successfully reported this slideshow.
Upcoming SlideShare
×

# Feb6

446 views

Published on

• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

### Feb6

1. 1. Today :Warm Up Final exam review Binomials polynomials Classwork test friday on exponents andscientific notation
2. 2. Warm- Up Exercises1. Find the total area of the figure.2. What is the solution to:-4y -20 = -10x and -5x - 14 = -2y 4. Write any expression in which a monomial is 5. Simplify: multiplied by a binomial. 3m2(3m + 2n - 4p) 3. List 3 different types of Monomials.
3. 3. Multiplying Binomials#1: The Box Method (x + 4)(x + 2) *Reminder: When multiplying, add the exponents
4. 4. Multiplying Binomials ==The More Common Method for solving binomials is...
5. 5. Multiplying BinomialsWe know how to multiply a binomial by a monomial: a ( x + 2) = ax + 2aCan we use the distributive property to multiply a binomial by a binomial? Suppose a = (x + 1). How do we find this product: (x + 1) ( x + 2) ?Can we distribute (x + 1) across (x + 2) ? The answer is yes. First multiply (x + 1) ( x ). Then multiply (x + 1) ( 2 ) . (x + 1) (x + 2) = (x + 1) ( x ) + (x + 1) ( 2 ) (x2 + x) + (2x + 2) x2 + 3x + 2
6. 6. F.O.I.L.If we perform our distribution in this order, (x + 1)(x + 2) = x (x + 2) + 1 (x + 2)a useful pattern emerges. Distributing produces the sum of these four multiplications. First + Outer + Inner + Last "F.O.I.L" for short. (x + 1) (x + 2) = x ( x + 2 ) + 1 ( x + 2 ) x2 + 2x + x + 2 x2 + 3x + 2
7. 7. Multiplying Binomials Mentally Can you see a pattern?(x + 2)(x + 1) x2 + x + 2x + 2 x2 + 3x + 2(x + 3)(x + 2) x2 + 2x + 3x + 6 x2 + 5x + 6(x + 4)(x + 3) x2 + 3x + 4x + 12 x2 + 7x + 12(x + 5)(x + 4) x2 + 4x + 5x + 20 x2 + 9x + 20(x + 6)(x + 5) x2 + 5x + 6x + 30 x2 + 11x + 30 There are lots of patterns here, but this one (x + a)(x + b) = x2 + (a + b) x + ab enables us to multiply binomials mentally. Later we will use this pattern "in reverse" to factor trinomials that are the product of two binomials.
8. 8. Practice: Multiplying Binomials Mentally1. What is the last term when (x + 3) is multiplied by (x + 6) ? 18 18 = 6 times 32. What is the middle term when (x + 5) is multiplied by (x + 7) ? 12x 12 = 5 plus 73. Multiply: (x + 4) (x + 7) x2 + 11x + 28 4 plus 7 = 11 4 times 7 = 284. Multiply: (x + 7) (x + 4) x2 + 11x + 28 7 plus 4 = 11 7 times 4 = 28
9. 9. Positive and NegativeAll of the binomials we have multiplied so far have been sums ofpositive numbers. What happens if one of the terms is negative? Example 1: (x + 4)(x - 3) 1. The last term will be negative, because a positive times a negative is negative. 2. The middle term in this example will be positive, because 4 + (- 3) = 1. (x + 4)(x - 3) = x2 + x - 12 Example 2: (x - 4)(x + 3) 1. The last term will still be negative, because a positive times a negative is negative. 2. But the middle term in this example will be negative, because (- 4) + 3 = - 1. (x - 4)(x + 3) = x2 - x - 12
10. 10. Two NegativesWhat happens if the second term in both binomials is negative? Example: (x - 4)(x - 3) 1. The last term will be positive, because a negative times a negative is positive. 2. The middle term will be negative, because a negative plus a negative is negative. (x - 4)(x - 3) = x2 -7x +12Compare this result to what happens when both terms are positive: (x + 4)(x + 3) = x2 +7x +12 Both signs the same: last term positive middle term the same
11. 11. Sign Summary Middle Term Last Term(x + 4)(x + 3) positive positive(x - 4)(x + 3) negative negative(x + 4)(x - 3) positive negative(x - 4)(x - 3) negative positive Which term is bigger doesnt matter when both signs are the same, but it does when the signs are different.
12. 12. Remember, F.O.I.L can be used whenmultiplying any binomial by another binomial.
13. 13. Class Work:Handout on Multiplying Binomials