Topic: Multiplying PolynomialsEssential Questions: How can you use the distributive property to solve for multiplying polynomials?

Two Similar Approaches

1. Basic Distributive Property2. FOIL

Name:Date:Period:

Home-Learning Review:

1st method: Basic Distributive Property

Using the distributive property, multiply 2x(5x + 8)

-2x2 (3x2 – 7x + 10)

2x (5x + 8)

– 20x2

+ 16x= 10x2

= -6x4 + 14x3

Example #1:

Example #2:

Can you make a connection from a previous lesson?

What do you remember about multiplying monomials?

What do you do with the coefficients?

What about the exponents?

Pair-Practice:

1) r (5r + r2)

2) 5y (-2y2 – 7y)

3) -cd2 (3d + 2c2d – 4c)

Simplifying

4(3d2 + 5d) – d(d2 -7d + 12)

y(y- 12) + y(y + 2) + 25 = 2y (y + 5) - 5

4) 5n(2n3 + n2 + 8) + n(4 –n)

5) 2(4x – 7) = 5(-2x – 9) - 5

Pair-Practice:

What’s the GCF?

5x3 + 25x2 + 45x

The FOIL method is ONLY used when you multiply 2 binomials. It is an acronym and

tells you which terms to multiply.

2) Use the FOIL method to multiply the following binomials:

(y + 3)(y + 7).

2nd Method: FOIL

(y + 3)(y + 7). F tells you to multiply the FIRST terms

of each binomial.

y2

2nd Method: FOIL

(y + 3)(y + 7). O tells you to multiply the OUTER

terms of each binomial.

y2 + 7y

(y + 3)(y + 7). I tells you to multiply the INNER

terms of each binomial.

y2 + 7y + 3y

(y + 3)(y + 7). L tells you to multiply the LAST terms

of each binomial.y2 + 7y + 3y + 21

Combine like terms.y2 + 10y + 21

Remember, FOIL reminds you to multiply the:

First terms

Outer terms

Inner terms

Last terms

6) (7x – 4)(5x – 1)

7) (11a – 6b)(2a + 3b)

Pair-Practice:

Squaring a binomial

(x + 5)2

What does this mean? How do I

solve this type of Binomial?

8) (x – 3)2

Pair-Practice:

Challenge:

(6x2 – 2) (3x2 + 2x + 4)

6x2 (3x2 + 2x + 4)

– 2 (3x2 + 2x + 4)

(3x2 – 4x + 4) (2x2 + 5x + 6)3x2

– 4x

+ 4

(2x2 + 5x + 6)

(2x2 + 5x + 6)

(2x2 + 5x + 6)

10) (7x2 – 3x + 5) (x2 + 3x + 2)

9) (8x2 – 4) (2x2 + 2x + 6)

Pair-Practice:

Important:

•By learning to use the distributive property, you will be

able to multiply any type of polynomials.

• We need to remember to distribute each term in the first set of parentheses through

the second set of parentheses.

1. – x3 (9x4 – 2x3 + 7)2. (x+5)(x-7)3. (2x+4)(2x-3)4. (2x – 7)(3x2+x – 5)5. (x – 4)2

Time to work…independently.

Additional Practice:

Page 482 – 483 (1, 13, 14, 30)Page 489 – 490 (1, 3, 19, 38)

Page 495 – 496 (2, 3, 16, 30, 49)

HLA#2: Multiplying Polynomials

Page 483 (33)Page 489 – 491 (2, 18, 51)Page 496 – 497 (42, 59)