1. Multiplying Binomials
13-6
Multiplying Binomials
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra

2. Multiplying Binomials
13-6
Multiplying Binomials
Warm Up
Multiply.
1. x(x + 2)
2. –3(p – 4)
3. 2x(3x – 7)
4. Find the area of a rectangle with length 16 cm and width 21 cm.
x2 + 2x
–3p + 12
6x2 – 14x
336 cm2
Pre-Algebra

3. Multiplying Binomials
13-6
Multiplying Binomials
Problem of the Day
Find the missing term in the given arithmetic sequence.
170, , , , 140,. . .
162.5, 155, 147.5
Pre-Algebra

4. Multiplying Binomials
13-6
Multiplying Binomials
Learn to multiply binomials.
Pre-Algebra

5. Insert Lesson Title Here
13-6
Multiplying Binomials
Insert Lesson Title Here
Vocabulary
FOIL
Pre-Algebra

6. Multiplying Binomials
13-6
Multiplying Binomials
You can use the Distributive Property to multiply
two binomials.
(x + y)(x +z) = x(x + z) + y(x + z) =
x2 + xz + xy + yz
Pre-Algebra

7. (x + y)(x + z) = x + xz xy yz Multiplying Binomials 13-6
The product can be written as FOIL: The First terms, the Outer terms, the Inner terms, and the Last terms of the binomials.
First
Last
(x + y)(x + z) = x 2 + xz xy yz
( X + Y)(X + Z) = X
Inner
Outer
Pre-Algebra

8. Additional Example 1A & 1B: Multiplying Two Binomials
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Multiplying Binomials
Additional Example 1A & 1B: Multiplying Two Binomials
Multiply.
A. (n – 2)(m – 8)
B. (x + 3)(x + z)
(n – 2)(m – 8)
Foil
(x + 3)(x + z)
mn – 8n – 2m + 16
x2 + xz + 3x + 3z
Pre-Algebra

9. Additional Example 1C & 1D: Multiplying Two Binomials
13-6
Multiplying Binomials
Additional Example 1C & 1D: Multiplying Two Binomials
Multiply.
C. (a + 3)(a + 5)
D. (x – 4y)(x + 7y)
(a + 3)(a + 5)
Foil
(x – 4y)(x + 7y)
a2 + 5a + 3a + 15
x2 + 7xy – 4xy – 28y2
a2 + 8a + 15
Combine like terms.
x2 + 3xy – 28y2
Pre-Algebra

10. Multiplying Binomials
13-6
Multiplying Binomials
When you multiply two binomials, you will always get four products. Then look for like terms to combine.
Helpful Hint
Pre-Algebra

11. Insert Lesson Title Here
13-6
Multiplying Binomials
Insert Lesson Title Here
Try This: Example 1A & 1B
Multiply.
A. (r – 4)(s – 6)
B. (y + 2)(y + r)
(r – 4)(s – 6)
Foil
(y + 2)(y + r)
rs – 6r – 4s + 24
y2 + ry + 2y + 2r
Pre-Algebra

12. Insert Lesson Title Here
13-6
Multiplying Binomials
Insert Lesson Title Here
Try This: Example 1C & 1D
Multiply.
C. (a + 3)(a + 4)
D. (x – 3y)(x + 8y)
(a + 3)(a + 4)
Foil
(x – 3y)(x + 8y)
a2 + 4a + 3a + 12
x2 + 8xy – 3xy – 24y2
a2 + 7a + 12
Combine like terms.
x2 + 5xy – 24y2
Pre-Algebra

13. Multiplying Binomials
13-6
Multiplying Binomials
Additional Example 2
An 8 in. by 10 in. photo has a wooden frame that extends x in. beyond each side. Represent the area of the frame in terms of x.
Base: 8 + 2x Height: x
Area of the photo and frame combined:
A = (8 + 2x)(10 + 2x)
= x + 20x + 4x2
= x + 4x2

14. Multiplying Binomials
13-6
Multiplying Binomials
The photo area is 8 · 10 = 80 in2, so the
frame area is x + 4x2 – 80 = x + 4x2 in2.

15. Insert Lesson Title Here
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Multiplying Binomials
Insert Lesson Title Here
Try This: Example 2
Find the area of the border of a computer screen of width x centimeters around a 50 cm by 80 cm screen. Represent the area of the border in terms of x.
Base: x Height: x
Area of the screen and border combined:
A = (80 + 2x)(50 + 2x)
= x + 100x + 4x2
= x + 4x2

16. Multiplying Binomials Insert Lesson Title Here
13-6
Multiplying Binomials
Insert Lesson Title Here
Try This: Example 2 Continued
The screen area is 80 · 50 = 4000 cm2, so the
frame area is x + 4x2 – 4000 = x + 4x2 cm2.

17. Multiplying Binomials
13-6
Multiplying Binomials
Binomial products of the form
(a + b)2, (a – b)2, and
(a + b)(a – b) are often called
special products.

18. Additional Example 3A & 3B: Special Products of Binomials
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Multiplying Binomials
Additional Example 3A & 3B: Special Products of Binomials
Multiply.
A. (x + 6)2
B. (n – m)2
(x + 6)2
(n – m)2
(x + 6)(x + 6)
(n – m)
x2 +6x + 6x + 36
n2 – nm – nm + m2
x2 + 12x + 36
n2 – 2nm + m2

19. Additional Example 3C: Special Products of Binomials
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Multiplying Binomials
Additional Example 3C: Special Products of Binomials
Multiply.
C. (x – 7)(x + 7)
(x – 7)(x + 7)
x2 + 7x – 7x – 49
x2 – 49

20. Insert Lesson Title Here
13-6
Multiplying Binomials
Insert Lesson Title Here
Try This: Example 3A & 3B
Multiply.
A. (x + y)2
B. (r – 3)2
(x + y)2
(r – 3)2
(x + y)(x + y)
(r – 3)
x2 + xy + xy + y2
r2 – 3r – 3r + 9
x2 + 2xy + y2
r2 – 6r + 9

21. Insert Lesson Title Here
13-6
Multiplying Binomials
Insert Lesson Title Here
Try This: Example 3C
Multiply.
C. (x – y)(x + y)
(x – y)(x + y)
x2 + xy – xy – y2
x2 – y2

22. Multiplying Binomials
13-6
Multiplying Binomials
Special Products of Binomials
(a + b)2 = a2 + ab + ab + b2 = a2 + 2ab + b2
(a – b)2 = a2 – ab – ab + b2 = a2 – 2ab + b2
(a + b)(a – b) = a2 – ab + ab – b2 = a2 – b2

23. Multiplying Binomials Insert Lesson Title Here
13-6
Multiplying Binomials
Insert Lesson Title Here
Lesson Quiz: Part 1
Multiply.
1. (x + 5)(x + 2)
2. (c – 4)(c – 2)
3. (2y + 2)(y – 3)
4. (2m + 2)(3n + 2)
x2 + 7x + 10
c2 – 6c + 8
2y2 – 4y – 6
6mn + 4m + 6n + 4

24. Multiplying Binomials Multiplying Binomials Insert Lesson Title Here
13-6
Multiplying Binomials
Pre-Algebra
13-6
Multiplying Binomials
Insert Lesson Title Here
Lesson Quiz: Part 2
Multiply.
5. (a – 1)2
6. (b + 3)(b – 3)
7. Find the area of a cement walkway of width w
yd that is around a 20 yd by 30 yd pool.
a2 – 2a + 1
b2 – 9
4w w