1. (2)(4) + (2)(5) + (3)(4) + (3)(5) =
Warm up:
(2 + 3)(4 + 5) =
(5)(9) = 45
(2)(4) + (2)(5) + (3)(4) + (3)(5) = = 45

2. Polynomials

3. Monomials (1 term) 4x
4x2
4x3y2

4. Binomials (2 terms)
4x + 2
4x2 + 3y
4x3y+2xy

5. Trinomials (3 terms)
4x2 + 2x + 5
10x2 + 3x + 6
4x3 + 2x2 + 5x

6. Multiplying Monomials

7. 4x 4x
(4x)(2x)
4 • 2 • x • x
8x2 -

8. 4x 4x
(-4x)(5x)
-4 • 5 • x • x
-20x2 -

9. 4x 4x
(-3x)(x)
-3 • x • x
-3x2 -

10. 4x 4x
(3x)(5)
3 • 5 • x
15x -

11. 4x 4x
(-7)(5x)
-7 • 5 • x
-35x -

12. Multiplying Binomials

13. – 4 3x
– 4 3x
(3x + 4)(2x + 3)

14. (2)(4) + (2)(5) + (3)(4) + (3)(5) =45
(2 + 3)(4 + 5) =
(5)(9) =
(2)(4) + (2)(5) + (3)(4) + (3)(5) = = 45

15. Distributive Property
– 4 3x
– 4 3x
Use the
Distributive Property
(3x + 4)(2x + 3)
6x2
+ 9x
+ 8x
+ 12
6x2 + 17x + 12

16. The FOIL Method (for multiplying binomials

17. First
(3x + 4)
(2x + 3)
6x2

18. Outside
(3x + 4)
(2x + 3)
6x2 + 9x

19. Inside
(3x + 4)
(2x + 3)
6x2+9x+8x

20. Last
(3x + 4)
(2x + 3)
6x2+9x+8x+12
6x2+17x+12

21. The method F O I L
(x + 5)(x – 2 ) + x²
+ -2x
+ 5x
+ -10
x² + 3x – 10

22. The method F O I L
(5x + 4)(2x + 2)
10x²
+ 10x
+ 8x
+ 8
10x² + 18x + 8

23. The method F O I L
(x + 3)(2x – 2 ) +
2x²
+ -2x
+ 6x
+ -6
2x² + 4x – 6

24. The method F O I L
(3x + 1)(3x + 3)
9x²
+ 9x
+ 3x
+ 3
9x² + 12x + 3

25. The method F O I L
(-x + 1)(-x + 3) x²
+ -3x
+ -1x
+ 3
x² - 4x + 3

26. The method F O I L (3a +2b)(a + 3b) 3a² + 11ab + 6b2 + 9ab 3a² + 2ab