Download Recall Worksheet R 6.7 Grouping like terms Like terms: • have the

Recall Worksheet R 6.7
Grouping like terms
Like terms:
• have the same pronumeral part
• can have different coefficients; 2x and 5x are like terms
• can have pronumerals in a different order; ab and ba are like terms
• can have pronumerals raised to exactly the same power; 7x3 and 4x3 are like terms.
Unlike terms:
• have different pronumeral parts; 2x and 2y are unlike terms
• can have the same pronumerals raised to different powers; x2 and x are unlike terms
• 2a and 2ab are unlike terms
Only like terms can be added or subtracted.
The expression 5a + 4b + a + 6b has four terms with two variables a and b. To simplify this expression we
add the a variables together and then the b variables together.
So: 5a + 4b + a + 6b = 5a + a + 4b + 6b = 6a + 10b
Parentheses are used to simplify expressions. 6(y + 2x) is the same as 6 × y + 6 × 2x. It can sometimes be
confusing to see a multiplication sign (×) and the pronumeral x so we remove the multiplication sign. To
expand parentheses we can draw lines to help us remember to multiply the term outside the brackets by the
term inside the brackets.
6(y + 2x)
= 6 × y + 6 × 2x
=6y + 12x
W orked Example 1
Simplify the expression by collecting like terms 10m + 5p + 8m
Thinking
Working
1
Find the like terms and perform the operation.
2
Simplify the expression.
10m and 8m are like terms
10m + 8m = 18m
10m + 5p + 8m
= 18m + 5p
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4576 2
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W orked Example 2
Simplify the expression by expanding and then collecting like terms 3(a + 2b) + 6b
Thinking
Working
1
3(a + 2b)
Expand the brackets first.
3 ( a + 2b)
= 3 x a + 3 x 2b
= 3 a + 6b
2
Collect like terms to simplify the expression.
1
Complete the grids by collecting like terms.
(a)
2
+
5m
8m
2m
m
3a + 6b + 6b
= 3a + 12b
(b)
–
4m
b
12m
5b
3m
14b
15m
20b
12b
15b
32b
18b
11b
Simplify each expression by collecting like terms.
(a) 4m + a + 6a + 10m = 4m + 10m + a + 6a = ___________m + __________a
(b) 7y – 12x – 2y – 6x = 7y – 2y – 12x – 6x = __________y – __________x
(c) 14e + 21f – 6e + 2f = 14e – __________ + 21f + __________ = __________e + __________f
(d) 103b – 48a – 5b + 22a = 103b ________ – 48a ________= __________a ________b
3
Simplify each expression by collecting like terms.
(a) 12ab + 4b + 5a + 6ab = __________________________________________________________
(b) 4mn + 2m + 5m – n = __________________________________________________________
(c) 32a + 14b + 22d – 16a = __________________________________________________________
(d) 5xy + 12x + 18xy – 2y + x = ________________________________________________________
4
Expand the brackets for the following expressions.
6(a +b)
(a)
= 6 × ________ + 6 × ________
10(m + n)
= 10 × ________ + 10 ×
_______
=_________ + _________
=_________ + _________
6(a + b)
(b)
10(m + n)
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4576 2
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2(2b +f)
(c)
2(2b + f)
9(9w + y)
= 2 × ________ + 2 × ________
(d)
9(9w + y)
=_________ + _________
5
=9 × ________ + 9 × ________
=_________ + _________
Expand the brackets for the following expressions and then collect like terms.
12(m – 4 d)+8m
(a)
12(m – 4d) + 8m
= 12 × ________ – 12 × ________ + 8m
=_________ – _________ + 8m
=_________ – _________ + _________
=_________ – _________
-2a(4 +6b)+24a
= -2 a × ________ + -2a × ________ + 24a
(b)
-2a(4 + 6b) + 24a
=_________ – _________ + 24a
=_________ – _________ + 24a
=_________ – _________
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4576 2
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