Topics
4. Algebra and Matrices
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AustraliaWA
Year 11

4.01 Algebra simplification

Lesson
Worksheet
Practice
Worksheet
Adding and subtracting like terms
1

State whether the following expressions are like terms:

a

11 p and 3 p

b

2 p and 15

c

9 p and 6 q

d

12 and 8

e

5 h and 5 h k

f

4 h^{4} and 3 h

g

8 h^{3} k^{4}and 9 k^{4} h^{3}

h

6 h^{k}and 7 k^{h}

2

Consider the expression: 3x+5x

a

Write the term 3x in expanded form.

b

Write the term 5x in expanded form.

c

Write 3x+5x as a sum of variables.

d

Simplify the expression.

3

Consider the expression: 6y-4y

a

Write the term 6y in expanded form.

b

Write the term -4y in expanded form.

c

Write 7y-4y as a sum and difference of variables.

d

Simplify the expression.

4

Simplify the following expressions:

a
10 x + 3 x
b
9 m - 7 m
c
9 k + 6 r - 8 k
d
7 x + 7 y - 3 y - 6 x
e
7 x + 4 y - 3 y - 5 x + 2
f
8x - 11y + 12x - 3y
g
4.7 v + 2.9 w + 1.1 v
h
\dfrac{3}{5} y + \dfrac{2}{5} k + 2 + \dfrac{1}{5} y
i
8 p - 6 q + 5 - 6 p + 6 q - 3
j
- 2 m + n - \left( - 7 m \right) - 3 n - 5 m + 9
k
5x^2-2x^2+6x^2
l
7y^3+4y+6y^3-9y
m
p^3+p^2+p+2p+3p
n
4x+6xy-11y+2x+9y-yx
Multiplying terms
5

Consider the expression: 2p\times 3q

a

Expand the term 2p into a product of a number and a variable.

b

Expand the term 3q into a product of a number and a variable.

c

Write 2p\times 3q as a product of numbers and variables.

d

Simplify the expression.

6

Simplify the following expressions:

a
v \times v
b
9 t \times t
c
u \times 6 \times u
d
8 m \times 2 m
e
7 \times u \times v \times 9
f
\left( - 8 y \right) \times 3 \times 4 w
g
\dfrac{1}{4} r \times 12 s
h
9 a \times 5 u \times 10 t
i
2 a \times 4 b \times 4 b \times 2 a
j
\left( - 2 p q \right) \times 6 q \times \left( - 2 n \right)
k
9 y \times \dfrac{1}{9} \times 18 w
l
7xy \times 2x \times (-4y)
Algebraic fractions
7

Simplify the following expressions:

a
\dfrac{3 x}{5} - \dfrac{x}{7}
b
\dfrac{20 n}{5}
c
\dfrac{8 m}{32}
d
\dfrac{15 k}{20 k}
e
\dfrac{12 x y}{4 y}
f
\dfrac{18 k p}{24 k}
g
\dfrac{- 20 m}{4 m}
h
\dfrac{2 r s \times 8 t \times 5}{4 s \times 6 t}
i
\dfrac{\left( - 3 u \right) \times 2 v w}{8 v \times 9 u}
j
\dfrac{8xy}{-4x^2}
k
\dfrac{10x}{5x^2 y}
l
\dfrac{20x \times 3y \times 2z}{16x \times 9y}
8

Convert the expression 14 y w \div 2 y w to a fraction and then simplify.

Expanding brackets
9

Expand the following expressions:

a
4 \left(t + 6\right)
b
3 \left(6 + r\right)
c
\left(r + 3\right) \times 5
d
- 9 \left(r + 7\right)
e
- 6 \left(n - 4\right)
f
- \left( 5 - a \right)
g
- 9 \left(5 + 4 c\right)
h
- 8 \left( - 9 n - 5\right)
i
3 r \left( 9 s - 4\right)
j
7 u \left( 8 v - 3 w\right)
k
- m \left( 2 n - 15 p\right)
l
r \left(r + 5\right)
m
y \left(y - 9\right)
n
- m \left(m + 1\right)
o
t \left( 2 t - 14\right)
p
2 n \left(n - 14\right)
q
- 4 \left( 4 p - 3 q + 4 n\right)
r
2 m \left( 3 n - 5 p + 7\right)
s
- \left( 3 u + 5 a - 7 t \right)
10

Expand and simplify:

a
6 \left(y + 8\right) - 5 y - 3
b
2 x + 10 + 6 \left(x + 4\right)
c
3 x + 8 + 2 \left( 6 x + 2\right)
d
9 x - 2 - 3 \left(x + 4\right)
e
5 + 8 y \left(y + 6\right) - 4 y^{2}
f
8 u \left( 10 u + v\right) - 5
11

Expand the following expressions:

a
-\dfrac{u}{2}\left(3a - 5t + 9\right)
b
11 \left(\dfrac{m}{14} - 2 n + \dfrac{1}{5}\right)
12

Expand and simplify:

a
6 \left( 10 x + 8 y\right) - 6 \left( - 6 y - 6 x\right)
b
2 u \left( 3 u + 5 v\right) - u \left( 6 u + v\right)
c
5 w y \left(y + w\right) + 4 w y \left(y + 2\right)
d
6 p \left( 3 q r - 3\right) - \left( 4 p q r - 5 p\right)
Applications of algebraic expressions
13

Dylan purchased 3 pens, 4 pencils and a single note pad. The total cost of all these items was 3 x + 4 y + 5 dollars.

a

What does the variable y represent?

b

What does the variable x represent?

c

What does 5 represent?

14

Deborah earns \$25 per hour of work and is paid double for every hour worked on the weekend. At the end of a week, Deborah calculates her pay for that week to be 25 x + 50 y dollars.

a

What represents the number of hours Deborah worked during the weekdays?

b

What represents the number of hours Deborah worked during the weekends?

15

Mohamad and Valentina run a clothes business. Mohamad is able to sew 5 shirts an hour, while Valentina is able to sew 3 shirts an hour. The expression 6 \left(5 + 3\right) represents the total number of shirts the couple is able to produce in a six-hour period.

What does 5 + 3 represent?

16

Brad and Patricia are making paper cranes to decorate their room. Brad can make m an hour while Patricia can make n an hour. Brad spends 6 hours making cranes while Patricia spends 5 hours over the weekend.

Together they make a total of 6 m + 5 n paper cranes over the weekend.

a

What does 6 m represent?

b

What does 5 n represent?

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