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

13-6 Multiplying Binomials

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

Warm UpMultiply.

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

Problem of the Day

Find the missing term in the given arithmetic sequence.

162.5, 155, 147.5

170, , , , 140,. . .

Pre-Algebra


Learn to multiply binomials.

Pre-Algebra


Vocabulary

FOIL

Insert Lesson Title Here

Pre-Algebra


You can use the Distributive Property to multiplytwo binomials.

(x + y)(x +z) = x(x + z) + y(x + z) =

x2 + xz + xy + yz

Pre-Algebra


The product can be written as FOIL: The First terms, the Outer terms, the Inner terms, and the Last terms of the binomials.

2First Last

Inner

Outer

Pre-Algebra


Multiply.

Additional Example 1A & 1B: Multiplying Two Binomials

A. (n – 2)(m – 8) B. (x + 3)(x + z)

(n – 2)(m – 8) (x + 3)(x + z)

mn – 8n – 2m + 16 x2 + xz + 3x + 3z

Foil

Pre-Algebra


Additional Example 1C & 1D: Multiplying Two Binomials

Multiply.

C. (a + 3)(a + 5) D. (x – 4y)(x + 7y)

(a + 3)(a + 5) (x – 4y)(x + 7y)

a2 + 5a + 3a + 15 x2 + 7xy – 4xy – 28y2

Foil

a2 + 8a + 15 x2 + 3xy – 28y2

Pre-Algebra

Combine like terms.


When you multiply two binomials, you will always get four products. Then look for like terms to combine.

Helpful Hint

Pre-Algebra


Try This: Example 1A & 1B


Pre-Algebra

Multiply.

A. (r – 4)(s – 6) B. (y + 2)(y + r)

(r – 4)(s – 6) (y + 2)(y + r)

rs – 6r – 4s + 24 y2 + ry + 2y + 2r

Foil


Try This: Example 1C & 1D


Pre-Algebra

Multiply.

C. (a + 3)(a + 4) D. (x – 3y)(x + 8y)

(a + 3)(a + 4) (x – 3y)(x + 8y)

a2 + 4a + 3a + 12 x2 + 8xy – 3xy – 24y2

Foil

a2 + 7a + 12 x2 + 5xy – 24y2Combine like terms.


Base: 8 + 2x Height: 10 + 2x

Area of the photo and frame combined:

A = (8 + 2x)(10 + 2x)

= 80 + 16x + 20x + 4x2

= 80 + 36x + 4x2


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.

Additional Example 2

The photo area is 8 · 10 = 80 in2, so the frame area is 80 + 36x + 4x2 – 80 = 36x + 4x2 in2.


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: 80 + 2x Height: 50 + 2x

Area of the screen and border combined:

A = (80 + 2x)(50 + 2x)

= 4000 + 160x + 100x + 4x2

= 4000 + 260x + 4x2


Try This: Example 2 Continued


The screen area is 80 · 50 = 4000 cm2, so the frame area is 4000 + 260x + 4x2 – 4000 = 260x + 4x2 cm2.


Binomial products of the form (a + b)2, (a – b)2, and (a + b)(a – b) are often calledspecial products.


Multiply.

Additional Example 3A & 3B: Special Products of Binomials

A. (x + 6)2

(x + 6)2

(x + 6)(x + 6)

x2 +6x + 6x + 36

x2 + 12x + 36

B. (n – m)2

(n – m)2

(n – m)(n – m)

n2 – nm – nm + m2

n2 – 2nm + m2


Additional Example 3C: Special Products of Binomials

C. (x – 7)(x + 7)

(x – 7)(x + 7)

Multiply.

x2 + 7x – 7x – 49

x2 – 49


Try This: Example 3A & 3B


Multiply.

A. (x + y)2

(x + y)2

(x + y)(x + y)

x2 + xy + xy + y2

x2 + 2xy + y2

B. (r – 3)2

(r – 3)2

(r – 3)(r – 3)

r2 – 3r – 3r + 9

r2 – 6r + 9


Try This: Example 3C


C. (x – y)(x + y)

(x – y)(x + y)

Multiply.

x2 + xy – xy – y2

x2 – y2


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


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)

c2 – 6c + 8


2y2 – 4y – 6

6mn + 4m + 6n + 4

x2 + 7x + 10


Lesson Quiz: Part 2Multiply.

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.

b2 – 9

a2 – 2a + 1


4w2 + 100w

13-6Multiplying Binomials

Pre-Algebra


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