- The document discusses multiplying polynomials, including monomials, binomials, and trinomials. - It explains how to use the FOIL method (First, Outer, Inner, Last) to expand two binomials by multiplying the terms. - Examples are provided of multiplying various polynomials together and expanding binomial expressions using FOIL. Tile models are also used to visualize polynomial multiplication.

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9.2 Multiplying
Polynomials

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Review - Simplify
3x + 2y + 5x - 4y
x2 - 2x + 5x2 - 4x
2x2 - 5x + x2 +3x-7
7a + 5b- (3a + b)

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answers
3x + 2y + 5x - 4y
8x - 2y
x2 - 2x + 5x2 - 4x
6x2 - 6x

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answers
2x2 -5x + x2 +3x -7
3x2 - 2x - 7
7a + 5b - (3a + b)
7a + 5b -3a - b
4a + 4b

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Objective
•To multiply
monomials and
binomials.
•To use the FOIL
method to expand
two binomials.

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A monomial has 1
term.
-3 X 5X2
monorail
1 rail

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A binomial has 2
unlike terms.
2X - 3 x + b
X2 - X n + 3
bicycle

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

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Multiply
x ( 4x ) = 4 X2
3 ( 5x ) = 15 x

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5x ( X + 2)
Distribute
= 5x2 + 10x
-3 (X - 2) = -3X + 6

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Tile models can
be used to visualize
a product.
Think of area.

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X
X A = l w
X2
1
X
x•x = x2
1•x = x
1
1
1•1= 1
x
1

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

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(X + 3)(X +2)
F irst O uter
I nner L ast
to multiply

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(X + 3)(X +2)
X2
F
+2X
O
+3X
I
+6
L
X2 + 5X + 6

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+
+
(X+2)(X+3)=X2+5X+6
X2 X X X
x
x
111
111
The
product
matches
the
model.

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Draw an area tile model
to show:
Your Turn
( X + 1)( X + 4 )
x +4
x
+
1
draw
the
lines

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+
+
A = (X + 1)(X + 4)

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(X + 1)(X + 4)
X2
First
+4X
Outer
+1X
Inner
+4
Last
X2 + 5X + 4
Expand

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

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Expand (x + 3)2=
(x +3)(x + 3)
x2 +3x + 3x + 9
x2 +6x + 9

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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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Multiply (x - 2)(x - 3)
X2 -3X -2X +6
= X2 - 5X + 6
foiled
again !

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Find (3x -2)(2x +3)
F
6X2
O
+9X
I
-4X
L
-6
= 6X2 +5X - 6

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( 5 + √7 ) (√7 - 2) =
_ _
5 √7 - 10 + 7 - 2 √7 =
F O I L
_ _
combine like terms
3 √7 - 3

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(w + 3) (w - 3)=
You try these
(2x + 5) (x - 2)=

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(2x + 5) (x - 2)
= 2x2 - 4x + 5x - 10
First Outer Inner Last
2X2 + X - 10

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(w + 3) (w - 3)
w2 – 3w + 3w - 9
=
= w2 - 9

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(3 - 5rs) (2r + 5s)
=
6r + 15s - 10r2s - 25rs2
Last one
Curses !
Foiled Again

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Do your
homework!
The key to
freedom is
courage.