Download Literal Equations

Name
Multiplication Review
February 22, 2016
Literal Equations
1) Solve the following equation for y:
y – 2 = ½ (x – 8)
2) Solve the following equation for c:
cd – ce = f
3) Solve the following equation for s:
sw – s = H
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Name
Multiplication Review
February 22, 2016
Multiplying Polynomials
Common Core Algebra 1
Polynomials, as we saw in last lesson, behave a lot like integers. We saw that, just like integers, adding one
polynomial to a 2nd polynomial results in a 3rd polynomial. The same will occur when multiplying them.
Exercise #1: Monomails are the simplest of polynomials. They only consist of 1 term. Remember terms are
separated by addition or subtraction. Find the following products of monomials:
(a) 5x3(2x2)
(b) -3x·-8x
(c) ½ x2y5 · ¾ x9y
We have also used the Distributive Property in previous lessons to multiply polynomials that are more
complicated.
Exercise #2: Find each of the products in simplest form by using the distributive property.
(a) 2x(3x -1)
(b) x2(4x2 + 3)
(c) -2x2y3(2xy – 5x)
(d) (x + 2)(x – 6)
(e) (2x + 7)(x + 3)
(f) (3x – 2)(5x – 1)
x(x – 6) + 2(x – 6)
x2 – 6x + 2x – 12
x2 – 4x -12
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Name
Multiplication Review
February 22, 2016
Never forget that as we do these manipulations we are using properties of equality to produce equivalent
expressions.
Exercise #3: Consider the product of two binomials (x -1)(x – 3)
(a) Find the product and express it as a
(b) Use your calculator to fill in tables. Are they equivalent? ____
trinomial polynomial written in standard
form. Write the product at the top of the 3rd
x
(x - 1)(x - 3)
row in table (b).
0
1
2
3
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Used properly, the Distributive Property can be used to find more complicated products.
Exercise #4: Find each of the following products
(a) (2x + 5)2
(b) (x + 2)(x2 + 4x + 3)
(c) (x – 4)(x + 3)(x – 5)
(d) (3x + 2)3
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Name
Multiplication Review
Exercise #5: Consider the product (3x + 2)(2x + 1)
(a) Write the product in standard form.
February 22, 2016
b) Use you calculator to fill in the tables. Are they
equaivalent?
x
(3x + 2)(2x + 1)
0
1
2
3
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Homework
1) Write the following products in terms of either x or t.
(a) 5x(2x – 4)
(b) 3t(t + 7)
(c) -4x(5x + 1)
2) Write each product as an equivalent polynomial written in standard form.
(a) (x + 5)(x – 3)
(b) (4x – 1)(x + 2)
(c) (6x – 5)(4x -3)
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Name
Multiplication Review
February 22, 2016
3) Squaring a binomial is also done using the distributive property. Write each as a trinomial in standard
form.
(a) (x + 3)2
(b) (x – 10)2
(c) (2t + 3)2
4. Conjugate binomials have the property of having the same terms but the operation between the two
terms is different. (One being addition and the other subtraction) Find each product and state the product in
standard form.
(a) (x+3)(x-3)
(b) (5t + 1)(5t – 1)
(c) (8 – 3t)(8 + 3t)
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Name
Multiplication Review
February 22, 2016
5) Write each product in standard polynomial form: (Hint: Look at Exercise #4)
(a) (x + 3)(x -3)(x – 8)
(b) (x + 2)(x – 2)(x + 3)(x – 3)
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