Multiply Binomials

(ax + b)(cx +d)

(ax + by)(cx +dy)

- ( x - 9 ) ≤ 5

-1 -1

x - 9 ≥ -5

+9 +9

x ≥ 4

+ ( x - 9) ≤ 5

x - 9 ≤ 5

+9 +9

x ≤ 14

Neg.

Pos.

less than is an “and” statementless than is an “and” statement

What kind of statement?

Write as one inequality4 ≤ x and x ≤ 14≤ x and x ≤ 14

4 ≤ x ≤14 4 ≤ x ≤14 GraphGraph

Don’t forget To flipsymbol

| x - 9 | ≤ 5

Graph 4 ≤ x ≤14

<---|---|---|---|---|---|---|---|---|---> 2 4 6 8 10 12 14 16 18

Now shade

Between the

circles !!

What kind of

Circles?

6. A savings account is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. If an investment of $2,000 accumulate $360 of interest in the checking accounting after 4 years, what was the annual simple interest rate on the savings account?

I = PRT 360= 360 = (2,000)(4)R 360 = 8,000 R

8,000 8,000

0.045 = R

4.5% = R

Interest paid by bank Principle (invested) Rate is unknown Time is 4 years Regroup & Multiply Divide Change to %

(2,000) (R)(4)

FOIL or use Distributive Property

1. (3x + 4)(5x +1) Distribute the 3x Multiply (don’t

forget to add exponents when multiplying)

Distribute the 4 Like terms

add-same sign coefficients only (don’t add exp.)

3x20x 4

215 23 4x x

215x

FOIL or use Distributive Property

#2) (2x + 5)(3x +7) Distribute the 2x Multiply (don’t

forget to add exponents when multiplying)

Distribute the 5 Like terms

add-same sign coefficients only (don’t add exp.)

26x 14x15x 35

26 29 35x x

FOIL or use Distributive Property

#3) (4x + 5)(3x -8) Distribute the 4x Multiply (don’t

forget to add exponents when multiplying)

Distribute the 5 like terms

subtract- opposite signs coefficients only (don’t add exp.)

=12x2 - 32x

+15x - 40

=12x2 – 17x - 40

FOIL or use Distributive Property

#4) (3x - 2)(5x + 3) Distribute the 3x Multiply (don’t

forget to add exponents when multiplying)

Distribute the -2 like terms

subtract- opposite signs coefficients only (don’t add exp.)

=15x2

- 10x - 6

=15x2 – 1x - 6

+9x

FOIL or use Distributive Property

#5) (3x - 2)(2x - 7) Distribute the 3x Multiply (don’t

forget to add exponents when multiplying)

Distribute the -2 like terms

Add- same signs coefficients only (don’t add exp.)

=6x2 - 21x

- 4x + 14

=6x2 – 25x + 14

FOIL or use Distributive Property

#6) (4x - 8)(2x - 3) Distribute the 4x Multiply (don’t

forget to add exponents when multiplying)

Distribute the -8 like terms

Add- same signs coefficients only (don’t add exp.)

=8x2 - 12x

- 16x + 24

=8x2 – 28x + 24

FOIL or use Distributive Property

#7) (4x – 2y)(4x – 3y) Distribute the 4x Multiply (don’t

forget to add exponents when multiplying)

Distribute the -2y like terms add -

same signs coefficients only (don’t add exp.)

=16x2 - 12xy

- 8xy + 6y2

=16x2 – 20xy + 6y2

FOIL or use Distributive Property

#8) (2x + 9y)(3x + 2y) Distribute the 2x Multiply (don’t

forget to add exponents when multiplying)

Distribute the 9y Like terms

add-same sign coefficients only (don’t add exp.)

=6x2 + 4xy

+ 27xy + 18y2

=6x2 + 31xy + 18y2

FOIL or use Distributive Property

#9) (2x + 5y)(4x - 9y) Distribute the 2x Multiply (don’t

forget to add exponents when multiplying)

Distribute the 5y like terms

subtract- opposite signs coefficients only (don’t add exp.)

=8x2 - 18xy+ 20xy - 45y2

=8x2 + 2xy - 45y2

FOIL or use Distributive Property

10) (4x - 5y)(5x + 6y) Distribute the 4x Multiply (don’t

forget to add exponents when multiplying)

Distribute the -5y like terms

subtract- opposite signs coefficients only (don’t add exp.)

=20x2 + 24xy - 25xy - 30y2

=20x2 - xy - 30y2

(x-8)2 =

11) (x - 8)(x - 8) Distribute the x Multiply (don’t

forget to add exponents when multiplying)

Distribute the -8 like terms

Add- same signs coefficients only (don’t add exp.)

=x2- 8x

- 8x + 64

=x2 – 16x + 64

Write it twice!!!!!!!!

(x-8) (x-8)

(x+2)2 =

12) (x + 2)(x + 2) Distribute the x Multiply (don’t

forget to add exponents when multiplying)

Distribute the 2 like terms

Add- same signs coefficients only (don’t add exp.)

= x2 + 2x

+ 2x + 4

= x2 + 4x + 4

Write it twice!!!!!!!!

(x+2) (x+2)

(3x2+ ½ )2 =

(3x2+ ½ ) (3x2+ ½ ) Distribute the 3x2

Multiply (don’t forget to add exponents when multiplying)

Distribute the ½ like terms

Add- same signs coefficients only (don’t add exp.)

= 9x4

Write it twice!!!!!!!!

23

2x

23

2x

1

4

4 26 19

2 4x x

4 2 19 3

4x x

14) (2x2 – ¼ )2

(2x2 - ¼ ) (2x2 - ¼ ) Distribute the 2x2

Multiply (don’t forget to add exponents when multiplying)

Distribute the ¼ like terms

Add- same signs coefficients only (don’t add exp.)

= 4x4

Write it twice!!!!!!!!

22

4x

22

4x

1

16

4 24 14

4 16x x

4 2 14

16x x