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. 

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From Algebra in 15 Minutues A Day. Copyright © 2009 by LearningExpress, LLC. All Rights Reserved.
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