Ch 10: PolynomialsB) Multiplying

Objective:

To multiply polynomials using various techniques.

Methods for Multiplying Polynomials

1) Distributive Property

2) Long Multiplication

3) FOIL (First, Outside, Inside, Last)

4) Algebra Tiles

Distributive Property

€

(x + 5)(2x − 3)

€

2x2 + 7x −15

x (2x – 3) +5(2x – 3)+

(2x2 – 3x) + (10x – 15)

(x + 3)(x + 4)

Distributive Property

Example 1 Example 2

x(x + 4) +3(x + 4)+

(x2 + 4x)+(3x + 12)

x2 +7x + 12

(2a − 1)(a − 5)2a(a − 5) −1(a − 5)+

(2a2 -10a)+(−a + 5)

2a2 -11a + 5

Long Multiplication

(x+5)(2x – 3)

€

−15

€

−3x

€

+10x

€

2x2

€

2x2

€

+7x

€

−15

*(x (2x (-3*5)(-3*x)

(2x*5)(2x*x)

+ 5)- 3)

Polynomial Squares

€

(x + 3)2

€

≠ x2 + 9 Common mistake!

€

(x + 3)2

€

=(x + 3)(x + 3)

€

x + 3

€

x + 3

€

+9

€

3x

€

+3x

€

x2

€

x2

€

+6x

€

+9

€

(x + 3)2 =

*

Long Multiplication

€

(2x + 5)2

€

2x + 5

€

2x + 5

€

+25

€

10x

€

+10x

€

4x2

€

4x2

€

+20x

€

+25

€

=(2x + 5)(2x + 5)

€

(3x − 4)2

€

3x − 4

€

3x − 4

€

+16

€

−12x

€

−12x

€

9x2

€

9x2

€

−24x

€

+16

€

=(3x − 4)(3x − 4)

* *

Example 1 Example 2

FOIL

(x+5) (2x – 3)

First: = 2x2

Outside: = -3x

Inside: = 10x

Last: 5 = -15

2x2 + 7x - 15

x 2x

x -3

5 2x

-3

FOIL

€

(y + 7)(y + 4)

€

(x + 3)(x − 8)

€

y2 +11y + 28

€

x2 − 5x − 24

Example 1 Example 2

y y

y 4

7 y

7 4

= y2

= 4y

= 7y

= 28

x x

x -8

3 x

3 -8

= x2

= -8x

= 3x

= -24

Algebra Tiles

€

2x2 + 7x −15

(x+5) (2x – 3)

x + 5

2x - 3

2

10 - 3 = 7

- 15

Totals

Algebra Tiles

€

(m + 2)(m + 8)

€

m2 +10m +16

Example 1 Example 2

m +2

m +

8

1 10 16

€

(x − 4)(x − 5)

€

x2 − 9x + 20

x − 4

x − 5

1 9 20

Classwork

1)

3)

2)

4)

€

(x + 6)(x − 4)

€

(t −10)(t + 6)

€

(x + 2)(x −11)

€

(2 + m)(7 − m)

€

x2 + 2x − 24

€

x2 − 9x − 22

€

t 2 − 4t − 60

€

14 + 5m − m2

5)

7)

6)

8)

€

(4t + 7)(4t − 7)

€

16t2 − 49

€

(m + 5)(m − 5)

€

m2 − 25

€

(2x + 3)(x + 6)

€

2x2 +15x +18

€

(k − 5)(2k − 7)

€

2k2 −17k + 35