Chapter 4 Algebra Worksheet Page 35
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C H A P T E R 4 : A L G E B R A
EXAMPLE 4F-2
Expanding and simplifying expressions
Expand and simplify each expression.
7p(3q + 4e)
2m(5m − 4)
a
b
THINK
WRITE
1 Use the distributive law. Multiply each term inside
7p(3q + 4e)
a
a
the brackets (3q and 4e) by the term in front of the
= 7p × 3q + 7p × 4e
brackets (7p).
2 Simplify by performing the multiplications. Write the
= 21pq + 28ep
pronumerals in each term in alphabetical order.
1 Multiply each term inside the brackets (5m and −4)
2m(5m − 4)
b
b
by 2m.
= 2m × 5m + 2m × (−4)
2
2 Simplify the multiplications.
= 10m
− 8m
Expand and simplify each expression.
4
a
a(b + 4)
b
x(3 + w)
c
d(c − e)
d
p(2m + q)
e
k(b − 4c)
f
t(3s + 5r)
g
2x(4y + 3w)
h
3a(2b − 4c)
9p(3q + 5k)
−8m(2n + 7w)
−4t(5a − 2b)
−5y(−3x − 4z)
i
j
k
l
4a(3a + 2)
6k(2k − 3)
3x(1 − 4x)
−2e(4e + 5)
m
n
o
p
2
2
2
q
−7n(n − 6)
r
−2b(2a − 3b)
s
5a
(2a − 3)
t
−11y(x
+ y
)
EXAMPLE 4F-3
Expanding and simplifying more complex expressions
Expand and simplify each expression.
a
4(2p + k − 3m)
b
−3(4xy + 7a − 1)
THINK
WRITE
a
1 Multiply each term inside the brackets
a
4(2p + k − 3m)
(2p, k and −3m) by the term in front of
= 4 × 2p + 4 × k + 4 × (−3m)
the brackets (4). Write negative terms in
brackets to see the operations clearly.
2 Simplify the multiplications.
= 8p + 4k − 12m
b
1 Multiply each term inside the brackets
b
−3(4xy + 7a − 1)
(4xy, 7a and −1) by −3.
= (−3) × 4xy + (−3) × 7a + (−3) × (−1)
2 Simplify the multiplications.
= −12xy − 21a + 3
Expand and simplify each expression.
5
a
2(3x + y + 7)
b
5(2ab + 4d − 3)
c
7(2c − d + 5ef )
d
−6(3g − 2h + gh)
e
−4(5k + 2km − 9)
f
−3(2xy + 4 − 7w)
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