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MU123
Business Mathematics
Week 12
BOOK C, Unit 9
Expanding Algebra
Week 12
Learning Outcomes
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
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) = (a+b)c + (a+b)d.
Second, expand each of the (a + b) brackets on the right-hand side:
(a + b)(c + d)
= (a+b)c + (a+b)d
= ac + bc + ad + bd.
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.
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
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 – 3X -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
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

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