multiplying binomials 14-6 learn to multiply binomials

Multiplying Binomials14-6

Learn to multiply binomials.


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


Multiply.

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


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.


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

Helpful Hint


Example 2

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


Example 2

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.


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


Multiply.

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


Example 3: Special Products of Binomials

C. (x – 7)(x + 7)

(x – 7)(x + 7)

Multiply.

x2 + 7x – 7x – 49

x2 – 49


Example 4

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


Example 4C

C. (x – y)(x + y)

(x – y)(x + y)

Multiply.

x2 + xy – xy – y2

x2 – y2


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz: Part I

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 II

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.

b2 – 9

a2 – 2a + 1

4w2 + 100w yd2


1. Multiply.(p + 7)(p + 8)

A. p2 + 15p + 56

B. p2 + 8p + 15

C. 2p2 + 8p + 15

D. 2p2 + 15p + 56



2. Multiply.(z – 3)(z – 5)

A. 2z2 – 8p + 15

B. z2 – 5p – 8

C. 2z2 – 5p – 8

D. z2 – 8p + 15



3. Multiply.(v – 7)2

A. v2 – 14v + 49

B. 2v2 – 7v – 14

C. v2 – 7v – 14

D. 2v2 – 14v + 49



4. Identify the area of a frame of width x ft that is around a 10 ft by 4 ft glass panel.

A. 4x2 + 28x ft2

B. 2x2 + 20x ft2

C. 4x2 + 20x ft2

D. 2x2 + 28x ft2


multiplying binomials 14-6 learn to multiply binomials

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