Page 391 - Algebra 1

Exploration Modeling Products of Binomials Use algebra tiles to find the product of (2x + 2)(x + 3).
a. Make a rectangle using algebra tiles. Use the expressions (2x + 2) and (x + 3) to represent the length and width of the rectangle.
b. Multiply each term across the top by each term along the side.
c. Which two terms have a product of x2?
d. Why are there two x2 tiles?
e. How many x-tiles are there in all? Explain.
(x + 3)
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Materials
• algebra tiles
(x + 3)
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Math Reasoning
Connect What are the perimeter and area of a square with side lengths (x + 1)?
f. Which two terms have a product of 6?
g. Verify If a rectangle has width (x + 3) and length (2x + 2), will the
area be (2x + 2)(x + 3)?
h. Model Use algebra tiles to find the product of (x + 1)2.
Use the Distributive Property to find the product of two binomials. Every term in the first polynomial is multiplied by the second polynomial.
2 Using the Distributive Property
a. Find the product of (x + 7)(x + 3). SOLUTION
376 Saxon Algebra 1
Example
(x + 7)(x + 3)
x(x + 3) = x2 + 3x
7(x + 3) = 7x + 21
x2 +3x+7x+21 x2 + 10x + 21
Multiply the first term in the first binomial by the second binomial.
Multiply the second term in the first binomial by the second binomial.
Addthetwoproducts. Simplify.
(2x + 2) (2x + 2)