Chapter Eleven

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MU123
Business Mathematics Week 12 BOOK C, Unit 9
Expanding Algebra
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Learning Outcomes
Week 12

• After studying this unit, student should be able
  to
• find the sum of any arithmetic sequence
• prove simple number patterns involving square
  numbers
• multiply out pairs of brackets
• add, subtract, multiply and divide algebraic
  fractions

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2 Multiplying out pairs of brackets
2.1 Pairs of brackets

• We learned that to multiply out the brackets
  Multiply each term inside the brackets by the
  multiplier of the bracket.
• Solve these two examples 3m(-2n 3r-6) ,
  (n-1)n
• Solution -6mn 9mr - 18m, n2 -n
• Now, You can multiply out two brackets of the
  form (a b)(c d) in two steps, as follows
• First, keep (a b) as one expression and use it
  as the multiplier to expand the right bracket (c
  d),
• to obtain (a b)(c d) (ab)c (ab)d.
• Second, expand each of the (a b) brackets on
  the right-hand side
• (a b)(c d) (ab)c (ab)d
  ac bc ad bd.

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2 Multiplying out pairs of brackets
2.1 Pairs of brackets

• We have done the following
• The acronym FOIL may help you to remember the
  order in which these pairs are multiplied
• FOIL stands for
• (1) First ac,
• (2) Outer ad,
• (3) Inner bc,
• (4) Last bd.

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2 Multiplying out pairs of brackets
2.1 Pairs of brackets

• For example, you can use the strategy above to
  multiply out the product
• (2s - t)(u - 3v) Apply FOIL
• F 2s u 2su,
• O 2s (-3v) -6sv,
• I (-t) u -tu,
• L (-t) (-3v) 3tv.
• Then 2su - 6sv - tu 3tv
• Exercise multiply out the brackets (a
  2b)(3c - d)
• Solution 3ac - ad 6bc 2bd

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2 Multiplying out pairs of brackets
2.1 Pairs of brackets

• Exercise
• Multiply the following brackets
• (n - 2)(n 2)
• Solution n2 2n -2n -4 n2 4
• (x 3)2
• Solution (X 3)(X 3) X2 3 X -3X 9
  X2 -6X 9
• We can also use the first strategy to multiply
  out two brackets that
• contain more than two terms
• Multiply the following brackets (2a - b)(c -
  3d 2e)
• Solution 2a(c-3d 2e)-b(c-3d 2e)
• 2ac - 6ad 4ae - bc 3bd - 2be

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4 Manipulating algebraic fractions
4.1 Equivalent algebraic fractions

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4 Manipulating algebraic fractions
4.2 Adding and subtracting algebraic fractions

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4 Manipulating algebraic fractions
4.2 Adding and subtracting algebraic fractions

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4 Manipulating algebraic fractions
4.2 Adding and subtracting algebraic fractions

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4 Manipulating algebraic fractions
4.3 Multiplying and dividing algebraic fractions

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4 Manipulating algebraic fractions
4.3 Multiplying and dividing algebraic fractions

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• Thank you