By LearningExpress Editors
Updated on Oct 3, 2011
Review these concepts at Multivariable Expressions Study Guide.
Multivariable Expressions Practice Questions
Problems
Practice 1
Simplify each expression.
 x + 5y – 3x
 2p – 9p^{2} + 8r^{2} + 2p^{2}
 7s – (4s + 2t) + 10t
 2b^{3} + 6c – b^{3} – 5c
 j + k + l – 2j – 3k – 4l
 2(x + y) – 5x
 wv + w(v – 1)
 6f^{ 5}g + 3f^{ 2} – 4g – 3f^{ 5}g + g
 –9a^{2} + 5(2b + 3) – b
 4(k + m) – 9(3k – 2m) + k + m
Practice 2
Find the value of each expression when r = 3 and t = –2.
 3r^{2} + 4t
 –r + 5t – 2t + 9r
 6r – 3t^{2} + 4t – 2r
 4rt – 2r(8 + t)
Find the value of each expression when a = –3, b = 6, and c = 1.
 2a + 3b – 4c – (5a + 4b)
 4(a – b + 2c) + c(a – 3)
 3c^{2} – 3ab + b(3a + c)
 5b + 2b (c – a) + 3ab
Find the value of each expression when w = 1, x = –2, y = 3, and z = –4.
 6(3w + x) + 2y – 3(w – z)
Solutions
Practice 1
1.  This expression has two x terms and one y term. 
Combine the x terms: x –3x = –2x.  
The y term cannot be combined with anything, so x + 5y –3x simplifies to –2x + 5y.  
2.  This expression has one p term, two p^{2} terms, and one r^{2} term. 
Combine the p^{2} terms: –9p^{2} + 2p^{2} = –7p^{2}.  
The other terms cannot be combined, so 2p –9p^{2} + 8r^{2} + 2p^{2} simplifies to 2p –7p^{2} + 8r^{2}.  
3.  This expression has two s terms and two t terms. 
Combine the s terms: 7s –4s = 3s.  
Combine the t terms. Remember: the 2t term is subtracted, so it is negative:–2t + 10t = 8t.  
7s –(4s + 2t) + 10t simplifies to 3s + 8t.  
4.  This expression has two b^{3} terms and two c terms. 
Combine the b^{3} terms: 2b^{3} –b^{3} = b^{3}.  
Combine the c terms: 6c –5c = c.  
2b^{3} + 6c –b^{3} –5c simplifies to b^{3} + c.  
5.  This expression has two j terms, two k terms, and two l terms. 
Combine the j terms: j –2j = –j.  
Combine the k terms: k –3k = –2k.  
Combine the l terms: l –4l = –3l.  
j + k + l –2j –3k –4l simplifies to –j –2k –3l.  
6.  This expression has two x terms and one y term before we multiply. Use the distributive law to find 2(x + y). Multiply 2 by x and multiply 2 by y: 
2(x +y) = 2x + 2y  
The expression is now:  
2x + 2y –5x  
Combine the x terms: 2x –5x = –3x.  
2(x + y) –5x simplifies to –3x + 2y.  
7.  Use the distributive law to find w(v –1). Multiply w by v and multiply w by –1: 
w(v –1) = wv –w  
The expression is now:  
wv + wv –w  
Combine the wv terms: wv + wv = 2wv.  
wv + w(v –1) simplifies to 2wv –w.  
8.  This expression has two f^{5}g terms, one f^{ 2} term, and two g terms. 
Combine the f 5g terms: 6f^{ 5}g –3f^{5}g = 3f^{5}g.  
Combine the g terms: –4g + g = –3g  
6f^{5}g + 3f^{2} –4g –3f^{5}g + g simplifies to 3f^{5}g + 3f^{2} –3g.  
9.  This expression has one a^{2} term, two b terms, and one constant term before we multiply 
Use the distributive law to find 5(2b + 3). Multiply 5 by 2b and multiply 5 by 3:  
5(2b + 3) = 10b + 15  
The expression is now:  
–9a^{2} + 10b + 15 –b  
Combine the b terms: 10b –b = 9b.  
–9a^{2} + 5(2b + 3) –b simplifies to –9a^{2} + 9b + 15.  
10.  This expression has three k terms and three m terms before we multiply. Use the distributive law to find 4(k + m). Multiply 4 by k and multiply 4 by m: 
4(k +m) = 4k + 4m  
Use the distributive law again to find –9(3k –2m). Multiply –9 by 3k and multiply –9 by –2m:  
–9(3k –2m) = –27k + 18m  
The expression is now:  
4k + 4m –27k + 18m + k +m  
Combine the k terms: 4k –27k + k = –22k.  
Combine the m terms: 4m + 18m + m = 23m.  
4(k + m) –9(3k –2m) + k + m simplifies to –22k + 23m. 

1
 2
View Full Article
From Algebra in 15 Minutues A Day. Copyright © 2009 by LearningExpress, LLC. All Rights Reserved.
Post a Comment
 No comments so far
Ask a Question
Have questions about this article or topic? Ask150 Characters allowed
Related Questions
See More QuestionsPopular Articles
Wondering what others found interesting? Check out our most popular articles.
 Kindergarten Sight Words List
 First Grade Sight Words List
 10 Fun Activities for Children with Autism
 Signs Your Child Might Have Asperger's Syndrome
 Theories of Learning
 A Teacher's Guide to Differentiating Instruction
 Child Development Theories
 Social Cognitive Theory
 Curriculum Definition
 Why is Play Important? Social and Emotional Development, Physical Development, Creative Development