Page 55 - Math Smart - 7

3.1.2 Simplifying algebraic expressions

In algebra, we can simplify long algebraic expressions, just like in fractions, by
grouping the like terms. What are like terms? ^ RECALL

Like terms In Stage 3, we learnt to
identify like fractions to
Like terms are terms that have the same variable(s) and each variable must
compare them.
have the same power/index.
and ^ are like
When two terms are not like terms, they are known as unlike terms.
fractions.
Sx + 5y + 7a: = 3x + 7x + 5y
Fill in the blank.
= lOx + 5y
Like terms Unlike terms
2x + 7x 2x + 7b
6m — 15m 6m — 15m^
14xy — 12xy 14xy - 12y
25a^ + 12a^ 25a^ + 12a^
4y + 7y 4y + 7
Think and Share

Example 5 Are 14xy and 12yx like
terms? Why?
Simplify the expressions.
x
a) 4a + 7a b) 9x - c) 3t — 25
d) 8a + 7b + 2a - 5b e) 3x + 4 - 2x -
f) 8a + 9b + 10c - 5 + 8b - 2a - 6c

Solution
a) 4a + 7a = 11a

b) 9x - X = 9x - Ix
= 8x X is the same as Ix

c) 3t-2s The terms are unlike terms so we
cannot simplify this expression
d) 8a + 7b + 2a - 5b = 8a + 7b + 2a — 5b Find the like terms Note that the sign in
front of each term stays
= 8a + 2a + 7b - 5b Group the like terms
with the term.
= 10a + 2b
t
= 2(5a + b) Simplify

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