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CHAPTER 10: Algebra: Basic algebra
Expand and simplify
This usually means that you need to expand more than one set of brackets and simplify the
resulting expressions.
You will often be asked to expand and simplify expressions.
EXAMPLE 9
Expand and simplify 3(4 + m) + 2(5 + 2m).
3(4 + m) + 2(5 + 2m) = 12 + 3m + 10 + 4m = 22 + 7m
EXAMPLE 10
Expand and simplify 3t(5t + 4) – 2t(3t – 5).
3t(5t + 4) – 2t(3t – 5) = 15t2 + 12t – 6t2 + 10t = 9t2 + 22t
Notice that multiplying –2t by –5 gives an answer of +10t.
EXAMPLE 11
Expand and simplify 4a(2b – 3f ) – 3b(a + 2f ).
4a(2b – 3f ) – 3b(a + 2f ) = 8ab – 12af – 3ab – 6bf = 5ab – 12af – 6bf
EXERCISE 10E
Simplify these expressions.
a
4t + 3t
b
2y + y
c
3d + 2d + 4d
d
5e – 2e
e
4p – p
f
3t – t
g
2t2 + 3t2
h
3ab + 2ab
i
7a2d – 4a2d
E
Expand and simplify these expressions.
a
3(4 + t) + 2(5 + t)
b
5(3 + 2k) + 3(2 + 3k)
c
4(1 + 3m) + 2(3 + 2m)
d
2(5 + 4y) + 3(2 + 3y)
e
4(3 + 2f ) + 2(5 – 3f )
f
5(1 + 3g) + 3(3 – 4g)
g
3(2 + 5t) + 4(1– t)
h
4(3 + 3w) + 2(5 – 4w)
Expand the expression
before trying to collect like
terms. If you try to expand
and collect at the same
time you will probably
make a mistake.
C
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