WU #19

1. Simplify: 4x2 – 2x + 4 + 3x2 + 4x – 1

2. Multiply: (x + 7)(x – 2)

3. Multiply: (3x + 9)(7x – 1)

4. Multiply: (x + 1)(x – 1)

5. Multiply: (2x - 5)(x – 4)

27 2 3x x

2 5 14x x

221 60 9x x 2 1x

22 13 20x x

5.10 Multiplying Binomials: Special Products

• Goal: To multiply the difference of two squares and square a binomial

Foil Multiply: (x + 3)(x – 3)

x2 – 3x + 3x - 9

x2 - 9

Difference of 2 SquaresThe product 0f

(A + B) and (A – B)

is always

The square of the first term minus the square of the

second.(a + b)(a – b) = a2 – b2

Multiply (Mental Math)(3x + 2)(3x – 2) =

9x2

(3x)2

(2)2

-(ALWAYS)

4

Multiply (Mental Math)

(x + 3)(x – 3) =

x2 - 9

Multiply (Mental Math)

(2x + 1)(2x – 1) =

4x2 - 1

Multiply (Mental Math)(2x3 + y)(2x3 – y) =

4x6 -

(2x3) =

(2x3)(2x3) =

2•2•x3•x3 4x6 – y2

Multiply (Mental Math)(4x4 + 3y)(4x4 – 3y)

=16x8 – 9y2

Multiply (Mental Math)(3x + 5)(3x – 5) =

9x2 - 25

Multiply (Mental Math)

1 12 2

5 5x x

2 14

25x

Multiply (Mental Math)

4 43 0.3 3 0.3x x

89 .09x

Multiply: (x + 3)2

x2 + 3x + 3x + 9

Multiplying a binomial by itself is called “squaring the

binomial”

x2 + 6x + 9

(x + 3)(x + 3)

Multiply: (x – 5)2

x2 - 5x - 5x + 25

Multiplying a binomial by itself is called “squaring the

binomial”

x2 - 10x + 25

(x -5)(x-5)

Square of a Binomial

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

(a - b)2 = a2 – 2ab + b2

Multiply

(x + 3)2 =

x2 + 6x + 9

Use the rule : (a+b)2 = a2 +2ab +b2

a=x and b = 3, plug it into the formula

x2 +2(x)(3) + 32

Multiply: Mentally Using the Formula

(2t - 5)2 =

4t2 +25- 20t

Multiply: Mentally Using the Formula

(2x + 7)2 =

4x2 + 28x + 49

Multiply: Mentally Using the Formula

(3x – 5y)2 =

9x2 - 30xy + 25y2

Multiply: Mentally Using the Formula

(4x3 – 3x)2 =

16x6 - 24x4 + 9x2

Assignment:

Page 247(2-40) even