WarmUp

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Warm-Up
Simplify.

• 2(x 4)
• -3(2 5x)
• 7(12 3x) 10
• (3x)(-4x)
• 3x (-4x)
• (4x2 6) (-x2 3x 4)
• (x3 2x2 3x 5) (x3 3x2 6)
• (b4 2b3 b 5) (3b3 b 5)

2x 8
-6 15x
74 21x
-12x2
-x
Add or subtract.
3x2 3x 2
x2 3x - 11
b4 b3
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Definitions

• Monomial
• Polynomial
• Binomial
• Trinomial

Number or product of numbers and variables with
whole number exponents
Monomial or sum or difference of monomials
A polynomial with two terms
A polynomial with three terms
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Genetics
Punnett Squares are diagrams used by scientists
to help them to figure out how inherited traits
(characteristics) will be distributed.
We will use something like a Punnett Square today
to help us learn how to multiply polynomials!!
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Multiplying Polynomials

• The Box Method

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The Box Method

• 1st Create a box

2nd Multiply
3rd Combine like terms
4th Write in Standard Form
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Example 1
(z 5) (z 3)
Place your terms in the first row and first
column.
Time to MULTIPLY.
3
z
z2
3z
z
-5z
-15
-5
Combine like terms and write in standard form.
Answer z2 2z - 15
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Multiplying Two BinomialsBox Method
(x 1)(x 2)

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Example 2
(2x2-4x5)(5x2-3x2)
Time to MULTIPLY.
Place your terms in the first row and first
column.
5x2
2
-3x
2x2
10x4
-6x3
4x2
-4x
-20x3
12x2
-8x
5
25x2
-15x
10
Combine like terms and write in standard form.
Answer10x4 26x3 41x2 23x 10
Will the box method work to find the product of a
binomial and a trinomial?
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Multiplying Two TrinomialsBox Method
(x2 2x - 1)(x2 - 3x 2)

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Multiplying Two BinomialsBox Method

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Multiplying Two TrinomialsBox Method

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Warm-Up

• What two numbers add up to 10 and their product
  is 25?

5 5 10, 5 x 5 25

• What two numbers add up to -5 and their product
  is 6?

-3 (-2) -5, (-3)(-2) 6

• What two monomials add up to -12x and their
  product is -45x2 ?

-15x 3x -12x, (-15x)(3x) -45x2

• What two monomials add up to 0 and their product
  is -9x2 ?

-3x 3x 0, (-3x)(3x) -9x2
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Factoring

• The Box and Diamond Method

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The Box and Diamond Method

• 1st Factor out any greatest common factor

2nd Create a box and a diamond
3rd Put first and last term diagonally in box
4th Put product of diagonal terms at top of
diamond
5th Put middle term at bottom of diamond (sum of
like terms)
6th Find two terms that multiply to the top
number and add to the bottom number
7th Put those numbers and terms in the box and
diamond
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Example 1
3x2 17x 10
5
x
Place your first and last terms in box diagonally.
3x2
15x
3x
Put product of diagonal terms at top of diamond.
2
10
2x
Put middle term at bottom of diamond.
30x2
15x
2x
17x
Time to FACTOR.
What two numbers multiply to the top number and
add to the bottom number??
Answer (3x 2)(x 5)
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Example 2
10x2 11x - 6
Put product of diagonal terms at top of diamond.
Place your first and last terms in box diagonally.
-60x2
15x
-4x
11x
Put middle term at bottom of diamond.
3
2x
What two numbers multiply to the top number and
add to the bottom number??
10x2
15x
5x
-2
-6
-4x
Time to FACTOR.
Answer (2x 3)(5x - 2)
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Factoring TrinomialsBox and Diamond Method