ObjectiveThe student will be able to:

use patterns to multiply special binomials.

SOL: A.2bDesigned by Skip Tyler, Varina High School

There are formulas (shortcuts) that work for certain polynomial

multiplication problems.

(a + b)2 = a2 + 2ab + b2

(a - b)2 = a2 – 2ab + b2

(a - b)(a + b) = a2 - b2

Being able to use these formulas will help you in the future when you have to factor. If you do not remember the formulas, you can always multiply

using distributive, FOIL, or the box method.

Let’s try one!1) Multiply: (x + 4)2

You can multiply this by rewriting this as (x + 4)(x + 4)

ORYou can use the following rule as a shortcut:

(a + b)2 = a2 + 2ab + b2

For comparison, I’ll show you both ways.

1) Multiply (x + 4)(x + 4)

First terms:

Outer terms:

Inner terms:

Last terms:

Combine like terms.

x2 +8x + 16

x +4

x

+4

x2

+4x

+4x

+16

Now let’s do it with the shortcut!

x2

+4x+4x+16

Notice you have two of

the same answer?

1) Multiply: (x + 4)2

using (a + b)2 = a2 + 2ab + b2

a is the first term, b is the second term(x + 4)2

a = x and b = 4Plug into the formula

a2 + 2ab + b2

(x)2 + 2(x)(4) + (4)2

Simplify.x2 + 8x+ 16

This is the same answer!

That’s why the 2 is in

the formula!

2) Multiply: (3x + 2y)2

using (a + b)2 = a2 + 2ab + b2

(3x + 2y)2

a = 3x and b = 2y

Plug into the formulaa2 + 2ab + b2

(3x)2 + 2(3x)(2y) + (2y)2Simplify

9x2 + 12xy +4y2

Multiply (2a + 3)2

1. 4a2 – 9

2. 4a2 + 9

3. 4a2 + 36a + 9

4. 4a2 + 12a + 9

Multiply: (x – 5)2

using (a – b)2 = a2 – 2ab + b2

Everything is the same except the signs!

(x)2 – 2(x)(5) + (5)2

x2 – 10x + 25

4) Multiply: (4x – y)2

(4x)2 – 2(4x)(y) + (y)2

16x2 – 8xy + y2

Multiply (x – y)2

1. x2 + 2xy + y2

2. x2 – 2xy + y2

3. x2 + y2

4. x2 – y2

5) Multiply (x – 3)(x + 3)

First terms:

Outer terms:

Inner terms:

Last terms:

Combine like terms.

x2 – 9

x -3

x

+3

x2

+3x

-3x

-9

This is called the difference of squares.

x2

+3x-3x-9

Notice the middle terms

eliminate each other!

5) Multiply (x – 3)(x + 3) using (a – b)(a + b) = a2 – b2

You can only use this rule when the binomials are exactly the same except for the sign.

(x – 3)(x + 3)

a = x and b = 3

(x)2 – (3)2

x2 – 9

6) Multiply: (y – 2)(y + 2)(y)2 – (2)2

y2 – 4

7) Multiply: (5a + 6b)(5a – 6b)

(5a)2 – (6b)2

25a2 – 36b2

Multiply (4m – 3n)(4m + 3n)

1. 16m2 – 9n2

2. 16m2 + 9n2

3. 16m2 – 24mn - 9n2

4. 16m2 + 24mn + 9n2