1. Lesson Objective: I will be able to …
Multiply polynomials
Language Objective: I will be able to …
Read, write, and listen about vocabulary, key
concepts, and examples

2. Example 1: Multiplying Monomials
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Example 1: Multiplying Monomials
Multiply.
A. (6y3)(3y5)
(6y3)(3y5)
Group factors with like bases together.
(6 3)(y3 y5) 
18y8
Multiply.
B. (3mn2) (9m2n)
(3mn2)(9m2n)
Group factors with like bases together.
(3 9)(m m2)(n2  n) 
27m3n3
Multiply.

3. When multiplying powers with the same base, keep the base and add the exponents.
x2  x3 = x2+3 = x5
Remember!

4. Group factors with like bases together. (3x3)(6x2)
Your Turn 1
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Multiply.
A. (3x3)(6x2)
Group factors with like bases together.
(3x3)(6x2)
(3 6)(x3 x2) 
Multiply.
18x5
B. (2r2t)(5t3)
Group factors with like bases together.
(2r2t)(5t3)
(2 5)(r2)(t3 t) 
10r2t4
Multiply.

5. Example 2: Multiplying a Polynomial by a Monomial
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Multiply.
4(3x2 + 4x – 8)
4(3x2 + 4x – 8)
Distribute 4.
(4)3x2 +(4)4x – (4)8
Multiply.
12x2 + 16x – 32

6. Example 3: Multiplying a Polynomial by a Monomial
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Multiply.
6pq(2p – q)
(6pq)(2p – q)
Distribute 6pq.
(6pq)2p + (6pq)(–q)
12p2q – 6pq2
Multiply.

7. Your Turn 3 Multiply. 3ab(5a2 + b) 3ab(5a2 + b) Distribute 3ab.
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Multiply.
3ab(5a2 + b)
3ab(5a2 + b)
Distribute 3ab.
(3ab)(5a2) + (3ab)(b)
15a3b + 3ab2
Multiply.

8. x2 3x 2x 6 x + 3 (x + 3)(x + 2) = x ● x = 3 ● x = x + 2
Another method for multiplying polynomials is called the Generic Rectangle. For example, the product of (x + 3)(x + 2) can be found by finding the area of a rectangle with a length of (x + 3) and a width of (x + 2).
Page 33 x
(x + 3)(x + 2) =
x ● x = x2
3 ● x = 3x x + 2
= x2 + 3x + 2x + 6
= x2 + 5x + 6
2 ● x = 2x
2 ● 3 = 6

9. To multiply a binomial by a binomial, you can apply the Distributive Property more than once:
(x + 3)(x + 2) = x(x + 2) + 3(x + 2)
Distribute x and 3.
Distribute x and 3 again.
= x(x + 2) + 3(x + 2)
= x(x) + x(2) + 3(x) + 3(2)
Multiply.
= x2 + 2x + 3x + 6
Combine like terms.
= x2 + 5x + 6

10. 1. Multiply the First terms. (x + 3)(x + 2) x x = x2
Another method for multiplying binomials is called FOIL.
Page 33 F
1. Multiply the First terms. (x + 3)(x + 2) x x = x2  O
2. Multiply the Outer terms. (x + 3)(x + 2) x 2 = 2x  I
3. Multiply the Inner terms. (x + 3)(x + 2) x = 3x  L
4. Multiply the Last terms. (x + 3)(x + 2) = 6 
(x + 3)(x + 2) = x2 + 2x + 3x + 6 = x2 + 5x + 6 F O I L

11. Example 4: Multiplying Binomials
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Example 4: Multiplying Binomials
Multiply.
(8m2 – n)(m2 – 3n)
Use the FOIL method.
8m2(m2) + 8m2(–3n) – n(m2) – n(–3n)
8m4 – 24m2n – m2n + 3n2
Multiply.
8m4 – 25m2n + 3n2
Combine like terms.

12. Example 5: Multiplying Binomials
Page 35
Example 5: Multiplying Binomials
Multiply.
Write as a product of two binomials.
(x – 4)2
(x – 4)(x – 4)
Use the FOIL method.
(x x) + (x (–4)) + (–4  x) + (–4  (–4)) 
x2 – 4x – 4x + 16
Multiply.
x2 – 8x + 16
Combine like terms.

13. Your Turn 5 Multiply. (a + 3)(a – 4) (a + 3)(a – 4)
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Multiply.
(a + 3)(a – 4)
(a + 3)(a – 4)
a(a) + a(–4) + 3(a) + 3(–4)
Distribute a and 3.
a2 – 4a + 3a – 12
Multiply.
a2 – a – 12
Combine like terms.

14. To multiply polynomials with more than two terms, you can use the Distributive Property several times. Multiply (5x + 3) by (2x2 + 10x – 6):
(5x + 3)(2x2 + 10x – 6) = 5x(2x2 + 10x – 6) + 3(2x2 + 10x – 6)
= 5x(2x2 + 10x – 6) + 3(2x2 + 10x – 6)
= 5x(2x2) + 5x(10x) + 5x(–6) + 3(2x2) + 3(10x) + 3(–6)
= 10x3 + 50x2 – 30x + 6x2 + 30x – 18
= 10x3 + 56x2 – 18

15. You can also use a rectangle model to multiply polynomials with more than two terms. This is similar to finding the area of a rectangle with length (2x2 + 10x – 6) and width (5x + 3):
2x2
+10x –6
10x3
50x2
–30x
30x
6x2
–18 5x +3
Write the product of the monomials in each row and column:
To find the product, add all of the terms inside the rectangle by combining like terms and simplifying if necessary.
10x3 + 6x2 + 50x2 + 30x – 30x – 18
10x3 + 56x2 – 18

16. Another method that can be used to multiply polynomials with more than two terms is the vertical method. This is similar to methods used to multiply whole numbers.
Multiply each term in the top polynomial by 3.
2x2 + 10x – 6
5x + 3 
Multiply each term in the top polynomial by 5x, and align like terms.
6x2 + 30x – 18
+ 10x3 + 50x2 – 30x
Combine like terms by adding vertically.
10x3 + 56x x – 18
10x3 + 56x2 – 18
Simplify.

17. Example 6: Geometry Application
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Example 6: Geometry Application
The width of a rectangular prism is 3 feet less than the height, and the length of the prism is 4 feet more than the height.
A. Write a polynomial that represents the area of the base of the prism.
A = l  w
A = l w 
Write the formula for the area of a rectangle.
Substitute h – 3 for w and h + 4 for l.
A = (h + 4)(h – 3)
A = h2 + 4h – 3h – 12
Multiply.
A = h2 + h – 12
Combine like terms.
The area is represented by h2 + h – 12.

18. Example 6: Geometry Application
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B. Find the area of the base when the height is 5 ft.
A = h2 + h – 12
A = – 12
Substitute 5 for h.
A = – 12
Simplify.
A = 18
The area is 18 square feet.

19. Classwork
Assignment #6
Holt 7-7 #2 – 24 even