Holt CA Course 1

12-6 Multiplying Binomials

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California StandardsCalifornia Standards

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Holt CA Course 1

12-6 Multiplying Binomials

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

Holt CA Course 1

12-6 Multiplying Binomials

Preview of Algebra 1 10.0 Students add, subtract, multiply, and divide monomials, and polynomials. Students solve multistep problems, including word problems, by using these techniques.

California Standards

Holt CA Course 1

12-6 Multiplying Binomials

Vocabulary

FOIL

Holt CA Course 1

12-6 Multiplying Binomials

You can use the Distributive Property to multiplytwo binomials.

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

x2 + xz + xy + yz

Holt CA Course 1

12-6 Multiplying Binomials

The product can be simplified using the FOIL method: multiply the First terms, the Outer terms, the Inner terms, and the Last terms of the binomials.

2First Last

Inner

Outer

Holt CA Course 1

12-6 Multiplying Binomials

Multiply.

Additional Example 1: 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

Holt CA Course 1

12-6 Multiplying Binomials

Additional Example 1: 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 – 28y2Combine like terms.

Holt CA Course 1

12-6 Multiplying Binomials

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

Helpful Hint

Holt CA Course 1

12-6 Multiplying Binomials

Check It Out! Example 1

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

Holt CA Course 1

12-6 Multiplying Binomials

Check It Out! Example 1

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.

Holt CA Course 1

12-6 Multiplying Binomials

Area of the frame = Total Area – Area of Photo

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

= 80 + 16x + 20x + 4x2

= 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 36x + 4x2 in2.

Total Area Area of Photo

– (8)(10)

– 80

Holt CA Course 1

12-6 Multiplying BinomialsCheck It Out! Example 2

Find the area of the border around a computer monitor of width x centimeters around a 50 cm by 80 cm screen. Represent the area of the border in terms of x.

Total Area

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

= 4000 + 160x + 100x + 4x2

= 260x + 4x2

The border area is 260x + 4x2 cm2.

Area of border = Total Area – Area of Screen

Area of Screen

– (50)(80)

– 4000

Holt CA Course 1

12-6 Multiplying Binomials

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

Holt CA Course 1

12-6 Multiplying Binomials

Multiply.

Additional Example 3: 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

Holt CA Course 1

12-6 Multiplying Binomials

Additional Example 3: Special Products of Binomials

C. (x – 7)(x + 7)

(x – 7)(x + 7)

Multiply.

x2 + 7x – 7x – 49

x2 – 49 7x – 7x = 0

Holt CA Course 1

12-6 Multiplying Binomials

Check It Out! Example 3

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

Holt CA Course 1

12-6 Multiplying Binomials

Check It Out! Example 3

C. (x – y)(x + y)

(x – y)(x + y)

Multiply.

x2 + xy – xy – y2

x2 – y2xy – xy = 0

Holt CA Course 1

12-6 Multiplying Binomials

Holt CA Course 1

12-6 Multiplying BinomialsLesson QuizMultiply.

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

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 yd2