10.2 – Multiplying Polynomials

I got polynomials….

They’re multiplying! And

I’m losing a binomial. Cause the power you’re

supplyin’, it’s terrifyin’.

Oh, you better distribute. Cause I need

an answer. And my calculator just won’t do.

Yeah, you better distribute, you better

understand, to my math, I must be true.

Warm-Up

Simplify the following expressions.1. (x + 4)22. -3(2 – 5x)3. 7(12 + 3x) – 104. (3x)(-4x)5. 3x + (-4x)

Homework Answers

20) -4; quadratic, trinomial

22) 5; quadratic, trinomial

24) 14; quartic, binomial

26) 7.4; cubic, binomial

28) 9; cubic, polynomial

30) -95; quartic, polynomial

32)

34)

36)

38)

a4 3a3 3a2 a

5y2 7

3x2 6x

7x4 x3 7x2 5x 9

Journal Entry

• Is the following statement true?

• Answer this question in journal form in your notebook.– Think about ways that you could check it.– Make a decision: Yes or no?• Defend your answer with 2-3 sentences.• Tweet about it later: #mathswagg

2( 4)( 5) 20 x x x

Discovery Activity

• Find the area of the large rectangle below!

5x cm 8 cm

2x cm

3 cm

***REMEMBER: AREA = LENGTH X WIDTH***

Solution(5x + 8)(2x + 3) = 5x·2x + 5x·3 + 8·2x + 8·3

= 10x2 + 15x + 16x + 24= 10x2 + 31x + 24

5x cm 8 cm

2x cm

3 cm

10x2 16x

15x 24

Multiplying Polynomials Using The Distributive Property

• Remember doing something like: 3(x - 5)?– This became: 3(x) + 3(-5)

• Which simplified to 3x - 15

• Now we are dealing with situations where we must do it twice!– Example: (4x – 9)(2x + 7)

• We simplify need to distribute all of the numbers in the first grouping to each of the numbers in the second grouping

Not just one number in front!

General Rule

(a + b)(c + d)

a(c + d) + b(c + d)

ac + ad + bc + bd

Example 1: iDo

(3a + 4)(2a + 1)Find the product.

Example 2: iDo

(x + 4)(x - 5)Find the product.

Example 3: WiiDo

(c - 3)(2c - 5)Find the product.

Example 4: WiiDo

(2w + 3)(2w - 3)Find the product.

Example 5: YouDo

(y + 5)(y + 7)Find the product.

Example 6: YouDo

(3x - 5)(5x + 2)Find the product.

So what if there’s a trinomial?

(a + b)(c + d + e) a(c + d + e) + b(c + d + e)ac + ad + ae + bc + bd + be

(a + b + c)(d + e) a(d + e) + b(d + e) + c(d + e)ad + ae + bd + be + cd + ce

Last Example

(t2 + 6t – 8)(t – 6)Find the product.

Boss/Secretary Practice• Students will work in pairs.• Materials: One worksheet, one calculator, one pencil per

pair• Students will be given one of two roles (you will

alternate these roles):– Boss: Tells the secretary how to solve the problem, is

the only one talking in the pair, does not write anything

– Secretary: Listens to the boss, writes everything, cannot talk unless (s)he is helping the boss

• Complete the worksheet in next before the end of class!

Homework

pg. 587 #18-46 every other even(#18, 22, 26, 30, 34, 38, 42, 46)