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Multivariable Expressions Practice Questions

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Updated on Oct 3, 2011

Review these concepts at Multivariable Expressions Study Guide.

Multivariable Expressions Practice Questions

Problems

Practice 1

Simplify each expression.

  1. x + 5y – 3x
  2. 2p – 9p2 + 8r2 + 2p2
  3. 7s – (4s + 2t) + 10t
  4. 2b3 + 6cb3 – 5c
  5.  j + k + l – 2j – 3k – 4l
  6. 2(x + y) – 5x
  7. wv + w(v – 1)
  8. 6f 5g + 3f 2 – 4g – 3f 5g + g
  9. –9a2 + 5(2b + 3) – b
  10. 4(k + m) – 9(3k – 2m) + k + m

Practice 2

Find the value of each expression when r = 3 and t = –2.

  1. 3r2 + 4t
  2. r + 5t – 2t + 9r
  3. 6r – 3t2 + 4t – 2r
  4. 4rt – 2r(8 + t)

Find the value of each expression when a = –3, b = 6, and c = 1.

  1. 2a + 3b – 4c – (5a + 4b)
  2. 4(ab + 2c) + c(a – 3)
  3. 3c2 – 3ab + b(3a + c)
  4. 5b + 2b (ca) + 3ab

Find the value of each expression when w = 1, x = –2, y = 3, and z = –4.

  1. 6(3w + x) + 2y – 3(wz)

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 p2 terms, and one r2 term.
  Combine the p2 terms: –9p2 + 2p2 = –7p2.
  The other terms cannot be combined, so 2p –9p2 + 8r2 + 2p2 simplifies to 2p –7p2 + 8r2.
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 b3 terms and two c terms.
  Combine the b3 terms: 2b3b3 = b3.
  Combine the c terms: 6c –5c = c.
  2b3 + 6cb3 –5c simplifies to b3 + 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) = wvw
  The expression is now:
  wv + wvw
  Combine the wv terms: wv + wv = 2wv.
  wv + w(v –1) simplifies to 2wvw.
8. This expression has two f5g terms, one f 2 term, and two g terms.
  Combine the f 5g terms: 6f 5g –3f5g = 3f5g.
  Combine the g terms: –4g + g = –3g
  6f5g + 3f2 –4g –3f5g + g simplifies to 3f5g + 3f2 –3g.
9. This expression has one a2 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:
  –9a2 + 10b + 15 –b
  Combine the b terms: 10bb = 9b.
  –9a2 + 5(2b + 3) –b simplifies to –9a2 + 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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