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Algebraic manipulation
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Browse Algebraic manipulation
44 questions at your level
Difficulty
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Level 1
Level 2
Level 3
Level 4
Level 5
Simplifying expressions
12 questions
Lesson
Not started
Mark as done
Simplify
3
a
+
5
a
−
2
a
3a + 5a - 2a
3
a
+
5
a
−
2
a
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Simplify
4
x
+
3
y
−
x
+
2
y
4x + 3y - x + 2y
4
x
+
3
y
−
x
+
2
y
●
●●●●
Level 1
2 marks
Start
→
Mark as done
Simplify
(a)
4
t
+
5
t
−
2
t
4t + 5t - 2t
4
t
+
5
t
−
2
t
(b)
3
g
×
4
h
3g \times 4h
3
g
×
4
h
●●
●●●
Level 2
2 marks
Start
→
Mark as done
Simplify
(a)
5
a
+
3
b
−
2
a
+
4
b
5a + 3b - 2a + 4b
5
a
+
3
b
−
2
a
+
4
b
(b)
4
c
×
3
c
2
4c \times 3c^2
4
c
×
3
c
2
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Simplify
(a)
m
5
×
m
3
m^5 \times m^3
m
5
×
m
3
(b)
12
n
7
÷
3
n
2
12n^7 \div 3n^2
12
n
7
÷
3
n
2
(c)
(
2
p
3
)
4
(2p^3)^4
(
2
p
3
)
4
●●●
●●
Level 3
3 marks
Start
→
Mark as done
Simplify
(a)
8
k
6
÷
2
k
3
8k^6 \div 2k^3
8
k
6
÷
2
k
3
(b)
w
4
×
w
×
w
3
w^4 \times w \times w^3
w
4
×
w
×
w
3
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Simplify fully
18
x
5
y
2
6
x
2
y
\dfrac{18x^5y^2}{6x^2y}
6
x
2
y
18
x
5
y
2
●●●●
●
Level 4
2 marks
Start
→
Mark as done
A rectangle has length
(
3
x
+
2
)
(3x + 2)
(
3
x
+
2
)
cm and width
(
2
x
−
1
)
(2x - 1)
(
2
x
−
1
)
cm.
(3x + 2) cm
(2x − 1) cm
Diagram NOT accurately drawn
Write an expression, in its simplest form, for the
perimeter
of the rectangle.
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Simplify fully
24
m
6
n
3
8
m
2
n
3
\dfrac{24m^6n^3}{8m^2n^3}
8
m
2
n
3
24
m
6
n
3
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Simplify
(
5
c
4
)
2
×
2
c
(5c^4)^2 \times 2c
(
5
c
4
)
2
×
2
c
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Simplify fully
(
3
a
2
b
)
3
×
2
a
b
2
6
a
4
b
3
\dfrac{(3a^2b)^3 \times 2ab^2}{6a^4b^3}
6
a
4
b
3
(
3
a
2
b
)
3
×
2
a
b
2
●●●●●
Level 5
3 marks
Start
→
Mark as done
Simplify fully
(
2
x
y
2
)
4
8
x
3
y
5
×
3
x
2
y
\dfrac{(2xy^2)^4}{8x^3y^5} \times 3x^2y
8
x
3
y
5
(
2
x
y
2
)
4
×
3
x
2
y
●●●●●
Level 5
3 marks
Start
→
Expanding brackets
18 questions
Lesson
Not started
Mark as done
Expand
3
(
x
+
4
)
3(x + 4)
3
(
x
+
4
)
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Expand
5
(
2
y
−
3
)
5(2y - 3)
5
(
2
y
−
3
)
●
●●●●
Level 1
1 mark
Start
→
Mark as done
(
x
+
5
)
2
(x + 5)^2
(
x
+
5
)
2
expands to
Circle your answer.
A
x
2
+
25
x^2 + 25
x
2
+
25
B
x
2
+
10
x
+
25
x^2 + 10x + 25
x
2
+
10
x
+
25
C
x
2
+
5
x
+
25
x^2 + 5x + 25
x
2
+
5
x
+
25
D
2
x
+
10
2x + 10
2
x
+
10
●
●●●●
Level 1
1 mark
Start
→
Mark as done
(a)
Expand
4
(
3
x
+
2
)
4(3x + 2)
4
(
3
x
+
2
)
(b)
Expand
x
(
x
−
6
)
x(x - 6)
x
(
x
−
6
)
●●
●●●
Level 2
2 marks
Start
→
Mark as done
Expand and simplify
3
(
2
x
−
1
)
−
2
(
x
+
4
)
3(2x - 1) - 2(x + 4)
3
(
2
x
−
1
)
−
2
(
x
+
4
)
(2 marks)
●●
●●●
Level 2
2 marks
Start
→
Mark as done
(a)
Expand and simplify
(
x
+
4
)
(
x
−
7
)
(x + 4)(x - 7)
(
x
+
4
)
(
x
−
7
)
(2 marks)
(b)
Factorise fully
6
x
2
−
9
x
6x^2 - 9x
6
x
2
−
9
x
(1 mark)
●●
●●●
Level 2
3 marks
Start
→
Mark as done
(a)
Expand and simplify
(
2
x
+
3
)
(
x
−
4
)
(2x + 3)(x - 4)
(
2
x
+
3
)
(
x
−
4
)
[2]
(b)
Factorise
4
x
2
−
25
4x^2 - 25
4
x
2
−
25
[1]
●●
●●●
Level 2
3 marks
Start
→
Mark as done
(a)
Expand
5
(
2
x
−
3
)
5(2x - 3)
5
(
2
x
−
3
)
(b)
Expand and simplify
3
(
2
x
+
1
)
−
2
(
x
−
4
)
3(2x + 1) - 2(x - 4)
3
(
2
x
+
1
)
−
2
(
x
−
4
)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
Expand and simplify
(
x
+
7
)
(
x
−
3
)
(x + 7)(x - 3)
(
x
+
7
)
(
x
−
3
)
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Expand and simplify
6
(
2
x
−
1
)
−
3
(
x
−
4
)
6(2x - 1) - 3(x - 4)
6
(
2
x
−
1
)
−
3
(
x
−
4
)
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Expand and simplify
(
2
x
−
5
)
2
(2x - 5)^2
(
2
x
−
5
)
2
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Expand and simplify
(
3
x
+
2
)
(
2
x
−
5
)
(3x + 2)(2x - 5)
(
3
x
+
2
)
(
2
x
−
5
)
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Expand and simplify
(
3
x
+
4
)
2
(3x + 4)^2
(
3
x
+
4
)
2
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Expand and simplify
(
4
x
−
3
)
(
2
x
+
5
)
(4x - 3)(2x + 5)
(
4
x
−
3
)
(
2
x
+
5
)
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Show that
(
3
x
+
2
)
(
x
−
4
)
(
x
+
6
)
(3x + 2)(x - 4)(x + 6)
(
3
x
+
2
)
(
x
−
4
)
(
x
+
6
)
can be written in the form
a
x
3
+
b
x
2
+
c
x
+
d
ax^3 + bx^2 + cx + d
a
x
3
+
b
x
2
+
c
x
+
d
where
a
a
a
,
b
b
b
,
c
c
c
and
d
d
d
are integers.
(3 marks)
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Expand and simplify
(
4
x
−
3
)
(
2
x
+
1
)
(
x
−
3
)
(4x - 3)(2x + 1)(x - 3)
(
4
x
−
3
)
(
2
x
+
1
)
(
x
−
3
)
(3 marks)
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Expand and simplify
(
x
+
1
)
(
x
−
2
)
(
x
+
4
)
(x + 1)(x - 2)(x + 4)
(
x
+
1
)
(
x
−
2
)
(
x
+
4
)
●●●●●
Level 5
3 marks
Start
→
Mark as done
Expand and simplify
(
x
+
3
)
(
x
−
1
)
(
x
−
5
)
(x + 3)(x - 1)(x - 5)
(
x
+
3
)
(
x
−
1
)
(
x
−
5
)
●●●●●
Level 5
3 marks
Start
→
Factorising with common factors
15 questions
Lesson
Not started
Mark as done
Factorise
4
x
+
12
4x + 12
4
x
+
12
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Factorise
x
2
+
5
x
x^2 + 5x
x
2
+
5
x
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Factorise fully
6
y
−
9
6y - 9
6
y
−
9
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Factorise
(a)
5
x
+
20
5x + 20
5
x
+
20
(b)
y
2
−
3
y
y^2 - 3y
y
2
−
3
y
●●
●●●
Level 2
2 marks
Start
→
Mark as done
(a)
Expand and simplify
(
x
+
4
)
(
x
−
7
)
(x + 4)(x - 7)
(
x
+
4
)
(
x
−
7
)
(2 marks)
(b)
Factorise fully
6
x
2
−
9
x
6x^2 - 9x
6
x
2
−
9
x
(1 mark)
●●
●●●
Level 2
3 marks
Start
→
Mark as done
Factorise
(a)
6
x
+
15
6x + 15
6
x
+
15
(b)
x
2
+
9
x
x^2 + 9x
x
2
+
9
x
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Factorise
fully
9
x
2
+
6
x
9x^2 + 6x
9
x
2
+
6
x
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Leah is trying to make
w
w
w
the subject of
y
=
w
4
−
6
y = \dfrac{w}{4} - 6
y
=
4
w
−
6
Here is her working.
y
+
6
=
w
4
y + 6 = \frac{w}{4}
y
+
6
=
4
w
4
×
y
+
6
=
w
4 \times y + 6 = w
4
×
y
+
6
=
w
w
=
4
y
+
6
w = 4y + 6
w
=
4
y
+
6
Leah's answer is wrong.
(a)
What mistake has Leah made?
(1 mark)
(b)
Factorise fully
6
a
2
b
−
15
a
b
2
6a^2b - 15ab^2
6
a
2
b
−
15
a
b
2
(2 marks)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
Factorise
fully
12
x
2
y
−
18
x
y
2
12x^2y - 18xy^2
12
x
2
y
−
18
x
y
2
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Factorise
(a)
y
2
−
49
y^2 - 49
y
2
−
49
(b)
4
a
2
−
25
b
2
4a^2 - 25b^2
4
a
2
−
25
b
2
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Mia says that
x
2
−
9
x^2 - 9
x
2
−
9
factorises as
(
x
−
3
)
2
(x - 3)^2
(
x
−
3
)
2
.
Explain why Mia is wrong, and factorise
x
2
−
9
x^2 - 9
x
2
−
9
correctly.
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Factorise
fully
20
a
3
b
2
−
15
a
2
b
4
20a^3b^2 - 15a^2b^4
20
a
3
b
2
−
15
a
2
b
4
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Factorise
81
−
16
m
2
81 - 16m^2
81
−
16
m
2
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Show that
(
2
n
+
1
)
2
−
(
2
n
−
1
)
2
(2n + 1)^2 - (2n - 1)^2
(
2
n
+
1
)
2
−
(
2
n
−
1
)
2
is a multiple of 8 for every whole number
n
n
n
.
●●●●●
Level 5
3 marks
Start
→
Mark as done
Show that
(
3
n
+
2
)
2
−
(
3
n
−
2
)
2
(3n + 2)^2 - (3n - 2)^2
(
3
n
+
2
)
2
−
(
3
n
−
2
)
2
is a multiple of 24 for every whole number
n
n
n
.
●●●●●
Level 5
3 marks
Start
→