copyright © 2013 pearson education, inc. section 1.8 simplifying and writing algebraic expressions
TRANSCRIPT
Copyright © 2013 Pearson Education, Inc.
Section 1.8
Simplifying and Writing Algebraic
Expressions
Terms
A term is a number, a variable, or a product of numbers and variables raised to powers.
Examples of terms include4, z, 5x, and −6xy2.
The coefficient of a term is the number that appears in the term.
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Example
Determine whether each expression is a term. If it is a term, identify its coefficient.
a. 97 b. 17x c. 4a – 6b d. 9y2 Solutiona. A number is a term. The coefficient is 97.b. The product of a number and a variable is a term. The coefficient is 17.c. The difference of two terms in not a term.d. The product of a number and a variable with an exponent is a term. Its coefficient is 9.
Page 72
Example
Determine whether the terms are like or unlike.
a. 9x, −15x b. 16y2, 1 c. 5a3, 5b3 d. 11, −8z
Solutiona. The variable in both terms is x, with the same power of 1, so they are like terms.b. The term 1 has no variable and the 16 has a variable of y2. They are unlike terms.c. The variables are different, so they are unlike terms.d. The term 11 has no variable and the −8 has a variable of z. They are unlike terms.
Page 72
Example
Combine terms in each expression, if possible.
a. −2y + 7y b. 4x2 – 6x
Solutiona. Combine terms by applying the distributive property.
−2y + 7y = (−2 + 7)y = 5y
b. They are unlike terms, so they can not be combined.
Page 73
Example
Simplify each expression.
a. 13 + z – 9 + 7z b. 9x – 2(x – 5)Solutiona. 13 + z – 9 + 7z b. 9x – 2(x – 5)
= 13 +(– 9) + z + 7z
= 13 +(– 9) + (1+ 7)z
= 4 + 8z
= 9x + (– 2)x + (−2)(– 5)
= 9x – 2x + 10
= 7x + 10
Page 74
Example
Simplify each expression.
a. 6x2 – y + 9x2 – 3y b.
Solutiona.
18 6
3
a
6x2 – y + 9x2 – 3y
= 6x2 + 9x2 + (–1y) + (–3y)
= (6 + 9)x2 + (–1+ (– 3))y
= 15x2 –4y
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Optional step
Example
Simplify each expression.
a. 6x2 – y + 9x2 – 3y b.
Solutionb.
18 6
3
a
18 6
3
a
18 6
3 3
a
6 2a
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18 6
3
a
3
263 a
6 2a
Example
A sidewalk has a constant width w and comprises several short sections with lengths 11, 4, and 18 feet. a. Write and simplify an expression that gives the number of square feet of sidewalk. b. Find the area of the sidewalk if its width is 3 feet. Solutiona. 11w + 4w + 18w
= (11 + 4 + 18)w= 33w
b. 33w = 33 ∙ 3 = 99 square feet
11 ft
4 ft
18 ft
w
Page 76
End of chapter problems
• do 56, 58, 72 on page 77
• do 74, 76, 78 on page 77-78
• do 80, 82 on page 78
• do 84, 86, 88 on page 78
DONE
Objectives
• Terms
• Combining Like Terms
• Simplifying Expressions
• Writing Expressions