1. What is the area of the shaded region?
Do Now:
What is the area of the shaded region?
What’s the formula for area, again?
x - 5
2x - 9

2. The 2nd method is the Box Method. This method works for every problem!
Here’s how you do it: (3x – 5)(5x + 2)
Draw a box. Write a polynomial on the top & side of a box.
It does not matter where.
This will be modeled in the next problem along with FOIL. 3x -5 5x +2

3. 3) Multiply (3x - 5)(5x + 2) 3x -5 5x +2 15x2 -25x +6x -10 15x2 +6x
First terms:
Outer terms:
Inner terms:
Last terms:
Combine like terms.
15x2 - 19x – 10 3x -5 5x +2
+6x
-25x
15x2
-25x
-10
+6x
-10
You have 2 techniques. Pick the one you like the best!

4. 4) Multiply (7p - 2)(3p - 4) 7p -2 3p -4 21p2 -6p -28p +8 21p2 -28p
First terms:
Outer terms:
Inner terms:
Last terms:
Combine like terms.
21p2 – 34p + 8 7p -2 3p -4
-28p
-6p
21p2
-6p +8
-28p +8

5. Multiply (y + 4)(y – 3) y2 + y – 12 y2 – y – 12 y2 + 7y – 12

6. Multiply (2a – 3b)(2a + 4b) 4a2 + 14ab – 12b2 4a2 – 14ab – 12b2
4a2 + 8ab – 6ba – 12b2
4a2 + 2ab – 12b2
4a2 – 2ab – 12b2

7. So, what if you have a binomial x trinomial?
Please copy:
(x + 3)(x² + 2x + 4)

8. Horizontal Method: (x + 3)(x² + 2x + 4)
 = x³ + 2x² + 4x + 3x² + 6x + 12 Write terms in descending order…
 = x³ + 2x² + 3x² + 4x + 6x + 12 
Combine like terms
= x³ + 5x² + 10x + 12  

9. x² + 2x + 4 x + 3 x³ + 2x² + 4x 3x² + 6x + 12 x³ + 5x² + 10x + 12
Vertical Method:
x² + 2x + 4
x + 3
x³ + 2x² + 4x
3x² + 6x + 12
x³ + 5x² + 10x + 12

10. OK, your turn… Please use whiteboard or your notebook: (x+1)(x²+2x+1)
(b2 + 6b –7)(3b – 4)
(2x2 + 5x –1)(4x – 3)
(2y – 3)(3y2 – y + 5)
(x2 + 2x + 1)(x + 2)