7-6 Multiplying Polynomials

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7-6 Multiplying Polynomials
Do you remember algebra tiles?
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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This piece is a 1
1
4
What is the total value of these pieces?
These pieces can be arranged differently.
Changing the arrangement does not change the area!
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This length is unknown.
The width of this piece is 1.
This piece is named by its area.
x
This piece is an x.
What is the total value of these pieces?
3x
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The length of this piece is x.
The width of this piece is x.
The area of this piece is x2.
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All of the yellow tiles we have used so far
represent positive values. To represent
negatives we will use the red side.
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Write an expression for the following and solve.
This is called the Zero Principle. Zero pairs
cancel each other.
Write an expression for the following and solve.
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In previous lessons, you added polynomials
Add the tiles.
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Algebra tiles can be used to model multiplying
polynomials.
Factors are represented on the outside of the
factor frame!
Factors are represented on the outside of the
factor frame!
x
The pieces of the rectangle inside the frame
represent the product!
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Negatives are represented by a red color.
x
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Today you will multiply a binomial by a binomial.
(x2)
The pieces of the rectangle inside the frame
represent the product!
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When negatives are involved, beware of zero pairs!
Remove zero pairs to find the product!
(x2)
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When not using algebra tiles, FOIL is a method
used to multiply a binomial times a binomial.
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Using the distributive property
Multiply the First terms
Plus multiply the Outer terms
Plus multiply the Inner terms
Plus multiply the Last terms
Combine like terms.
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Find the product.
Example 1
Example 2
Example 3
Example 4 Write an expression for the area of
the designer rug.
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Find the product.
Example 1
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Example 2
Change subtraction to addition to avoid sign
errors.
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Example 3 Find the product.
Change subtraction to addition to avoid sign
errors.
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Example 4 Write an expression for the area of
the designer rug.
Write formula for area of rectangle.
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The area of the rug is 6x2 x 2 units2.
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The area A of a trapezoid is one half the height
h times the sum of the bases, b1 and b2. Write
an expression for the area of the trapezoid.
The area of the trapezoid is
units2.
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The area of a triangle is one half the base b
times the height h. Write an expression for the
area of the triangle.
Example 5
Example 6
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Example 5 The area of a triangle is one half the
base b times the height h. Write an expression
for the area of the triangle.
The area of the triangle is 3x2 - 19x 14 units2.
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Example 6 The area of a triangle is one half the
base b times the height h. Write an expression
for the area of the triangle.
The area of the triangle is 4x2 - 2x 2 units2.
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Multiply a binomial with a trinomial.
Find the product.
Change subtraction to addition. Distribute the 2x
to the trinomial and then the -3.
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Example 7 Find the product.
Change subtraction to addition. Distribute the 6x
to the trinomial and then the -5.
Example 8 Find the product.
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Homework
7-A7 Pages 401-403 1831,3439,68-73.
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You can also multiply polynomials in a vertical
format.
Write in a vertical format change subtraction
to addition.
Multiply 5 to the top polynomial
Multiple 6x to the top polynomial
Combine like terms.
Line up like terms vertically!
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Example 8 Use a vertical format to find the
product.
Line up like terms vertically!