Test:
Algebraic expressions I - Challenging
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Question 1:
Simplify:
(
x
+
y
)
2
+
(
x
-
y
)
2
2
(
x
2
-
y
2
)
÷
1
x
3
-
y
3
-
3
x
y
A
(
x
-
y
)
2
B
x
-
y
C
1
D
x
2
-
y
2
Question 2:
Divide
x
4
-
7
x
3
+
5
x
2
+
6
x
-
7
by
x
+
1
A
x
3
-
8
x
2
+
10
x
-
7
B
x
3
-
8
x
2
+
13
x
-
7
C
x
3
-
8
x
2
+
13
x
-
5
D
x
3
-
8
x
2
-
7
Question 3:
Simplify:
x
-
2
-
2
x
-
3
x
-
3
-
1
A
{
-
1
,
x
∈
[
3
;
4
)
1
,
x
∈
(
4
;
+
∞
)
B
1
C
0
D
{
-
1
,
x
∈
[
3
;
4
)
1
,
x
∈
[
4
;
+
∞
)
Question 4:
Factorise:
x
3
-
4
x
2
+
8
x
-
5
A
(
x
-
1
)
(
x
2
-
2
x
+
5
)
B
(
x
-
1
)
(
x
2
-
3
x
+
2
)
C
(
x
-
1
)
(
x
2
-
3
x
+
5
)
D
(
x
-
1
)
(
x
-
2
)
(
x
-
3
)
Question 5:
Simplify:
18
x
4
3
÷
12
x
7
3
A
x
B
4
x
C
2
x
D
2
x
3
Question 6:
Simplify:
a
1
+
a
2
+
…
+
a
1000
a
-
1
+
a
-
2
+
…
+
a
-
1000
A
1
a
1001
B
a
1001
C
a
1000
D
1
a
1000
Question 7:
Factorise:
x
3
-
3
x
+
2
A
(
x
-
1
)
(
x
2
+
x
-
2
)
B
(
x
-
1
)
2
(
x
+
2
)
C
(
x
-
1
)
(
x
+
2
)
2
D
(
x
-
1
)
(
x
+
2
)
Question 8:
Simplify:
x
7
+
x
14
x
-
7
+
x
-
14
A
1
x
21
B
x
20
C
1
x
7
D
x
21
Question 9:
Simplify:
1
(
x
+
3
)
2
(
1
x
2
+
1
9
)
+
2
(
x
+
3
)
3
(
1
x
+
1
3
)
A
1
9
x
B
9
x
2
C
1
9
x
2
D
1
3
x
Question 10:
Reduce:
(
x
-
2
)
2
(
x
2
-
9
)
(
x
3
-
27
)
(
x
2
-
4
)
A
(
x
-
2
)
(
x
+
3
)
(
x
+
2
)
(
x
2
+
3
x
+
9
)
B
x
-
2
x
+
2
C
x
-
3
x
2
+
3
x
+
9
D
x
-
2
(
x
-
3
)
2
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