1. Multiplying Binomials Using the Distributive Property and
Recognizing the special case whose product is the Difference of Two Squares.

2. Simplify the sum. Write the answer in standard form.
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Simplify each product.
x (x-5)  3x (3x -4)  -6 (2x -5)  (4x +2)
Simplify the sum. Write the answer in standard form.
(x3 + 3x2 +x) + (5x2 +x + 1)

3. (x) (x+4) ? (-2) (x+4) ? What do we do to multiply What property do
we use to multiply
(-2) (x+4) ?

4. to multiply two binomials?
What do we do
to multiply two binomials?
(x-2) (x+4)

5. Use the distributive property twice to multiply two binomials.
Example: (x-3) (x-5)
= distribute x distribute -3
= (x)(x) + (x)(-5) (-3)(x) + (-3)(-5)
= x2 - 5x x +15
= x2 -8x +15

6. Simplify the products. (x +3) (x – 7) (2x -1)(x+2)
Show all your steps.
Find a partner.
Explain to your partner how you simplified your product.

7. How do you find the area of each figure?
(x+4)
(x+6)
(n+3)
(n-2)

8. How will you calculate the area of the blue shaded area?
Think, Pair, Share
How will you calculate the area of the blue shaded area?
Explain your solution to your partner.
(3x +2)
(x +6)
(x+3)
(x+2)

9. Shaded Area =Large Area – Small Area A = (3x +2) (x+6) - (x+3)(x+2)
This would be solution
Shaded Area =Large Area – Small Area
A = (3x +2) (x+6) - (x+3)(x+2)
A = (3x2 +18x +2x +12) –(x2 +2x +3x +6)
A =3x2 + 20x +12 –x2 -5x -6
A = 2x2 +15x +6

10. Five people work at the board please!
Each person find the product of one of the following:
(x+6)(x-6) (k+9)(k-9) (3c +7)(3c -7)
(y+8)(y-8) (2r-1)(2r +1)
Compare the pairs of binomials. What is similar?
Compare the solutions. What is similar?
Is there a pattern?
Can we predict the product of (x+4)(x-4)?

11. Rule: The Difference of Squares (a + b)(a – b) = a2 – b2
The product of the sum and the difference of the same two terms
is the difference of their squares.

12. Exit Pass Homework 1. Find the product. Show all your work.
(2x+7) (x-2)
2. This problem was easy, takes work, very difficult . Circle one.
3. What question do you have?
Homework
See Problem Set: choose your homework.

13. C. Find the area of each figure.
Show your work on a separate piece of paper.
(a+3)
(2x+5)
(x-4)
(x-1) g. a.
(2x-5) e.
(x+5)
(x-3) c.
(a-3) b.
(2x-4)
(3x+5)
(2a+5) h.
(2x+6)
(3x+1)
(x+4)
(x+6) d. f.
(n-2)
(n+12) i.

14. D. Find the area of each shaded region.
Show all your work on a separate piece of paper. Write your answers in standard form.
(2x+4)
(x+2)
(x+4)
(2x+8)
(x+8)
(3x+1)
(x-2) b. a. d.
(2x+1)
(x+6)
(3x+6)
(x) c.
(x+5)
(x)
(x+1)
(x+7)

15. E. The area in the shaded region is 72 – 22.
Cut out the figure.
Make a single cut across the shaded region and reassemble it to show that 72 – 22 = (7-2) (7+2).
Draw your reassembled figure.
Label its dimensions. 5 7 2

16. F. Word Problems G. Fast Forward x+4 x+8 2x-7 2x-3
1. The Cutting Edge frame shop makes a mat by cutting out the inside of a rectangular board. Use the diagram.
a. Find the length and width of the original board if the area of the mat (shaded) is 184 in2.
1. Simplify the product.
a. (x+4) (x2 +6x +3)
b. (n+2)(n+2)(n+2)
x+8
x+4
2x-3
2x-7
2. The formula V = 4/3  r3
gives the volume of a sphere.
Find the formula for a sphere that has a radius 3 more than r.
Simplify the expression.
Write your answer in standard form.
2. The Robertsons put a rectangular pool with stone walkway around it in their back yard. The total length of the pool and walkway is 3 times the total width. The walkway is 2 ft wide all around.
Draw a diagram of the pool and the walkway. Label the dimensions.
Write an expression for the area of the pool.
Find the area of the pool when the total width is 10 ft.
Find the area of the pool when the total width is 9 ft.