1. 9.2 Multiplying
Polynomials
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2. Review - Simplify x2 - 2x + 5x2 - 4x 2x2 - 5x + x2 +3x-7
3x + 2y + 5x - 4y
x2 - 2x + 5x2 - 4x
2x2 - 5x + x2 +3x-7
7a + 5b- (3a + b)
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3. combine like terms answers 3x + 2y + 5x - 4y 8x - 2y
x2 - 2x + 5x2 - 4x
6x2 - 6x
combine like terms
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4. answers 2x2 -5x + x2 +3x -7 3x2 - 2x - 7 7a + 5b - (3a + b)
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5. Objective To multiply monomials and binomials.
To use the FOIL method to expand two binomials.
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6. A monomial has 1
term.
X X2
monorail
1 rail
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7. A binomial has 2 unlike terms. 2X - 3 x + b X2 - X n + 3 bicycle
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bicycle

8. A trinomial has 3 unlike terms. x2 + 2x - 5 x + xy + y
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triangle 3 sides

9. Multiply
x ( 4x ) =
4 X2
3 ( 5x ) =
15 x
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10. Distribute
= 5x2 + 10x
5x ( X + 2)
-3 (X - 2)
= -3X + 6
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11. Tile models can be used to visualize a product. Think of area.
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12. X
A = l w
x•x = x2 X X2 x
1•x = x 1 X
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1•1= 1 1

13. + + A = (X + 2)(X + 3) Find an eq. for this tile model of area. 3 x x
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A = (X + 2)(X + 3)

14. (X + 3)(X +2)
F O I L
to multiply
O uter
F irst
L ast
I nner
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15. (X + 3)(X +2)
F O I L X2 F
+2X O
+3X I +6 L
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X2 + 5X + 6

16. X X X + X2 + x 111 (X+2)(X+3)=X2+5X+6 The product matches the model. 3
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17. Draw an area tile model to show:
( X + 1)( X + 4 )
x +4
Your Turn x + 1
draw
the
lines
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18. A = (X + 1)(X + 4) + 4 x x +
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19. (X + 1)(X + 4) X2 First +1X Inner +4 Last +4X Outer X2 + 5X + 4 Expand
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X2 + 5X + 4

20. Expand (x + 3)(x -5) F O I L
-15
+3X X2
-5X
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X2 - 2X - 15

21. Expand (x + 3)2=
(x +3)(x + 3)
x2 +3x + 3x + 9
x2 +6x + 9
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22. Expand (x + 4)(x - 3) First x2 Outer -3x Inner 4x Last -12
= x2 - 3x + 4x - 12
= x2 + x -12
Your Turn
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23. X2 -3X -2X +6 = X2 - 5X + 6 Multiply (x - 2)(x - 3) foiled again !
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24. Find (3x -2)(2x +3) F
6X2 O
+9X I
-4X L -6
= 6X2 +5X - 6
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25. ( 5 + √7 ) (√7 - 2) = F O I L _ _ 5 √7 - 10 + 7 - 2 √7 =
_ _
( 5 + √7 ) (√7 - 2) =
F O I L
_ _
5 √ √7 =
combine like terms
3 √7 - 3
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26. You try these
(2x + 5) (x - 2)=
(w + 3) (w - 3)=
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27. (2x + 5) (x - 2) 2x2 - 4x + 5x - 10 = First Outer Inner Last
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28. (w + 3) (w - 3) =
w2 – 3w + 3w - 9 =
w2 - 9
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29. (3 - 5rs) (2r + 5s) = 6r + 15s - 10r2s - 25rs2 Last one Curses !
Foiled Again
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30. Do your
homework!
The key to
freedom is
courage.
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