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Quadratic Expressions and Equations Video Questions and Answers
If the expression
25
y
2
-
70
y
+
d
is a perfect square, where d is a constant, find the value of d
(1m 57s)
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1.
Factorize completely
a
2
+
15
a
b
+
36
b
2
2.
Simplify
(
6
a
+
b
)
(
a
+
b
)
-
7
b
(
a
+
b
)
2
a
2
-
2
b
2
3.
Simplify
a
2
(
a
+
b
)
+
b
2
(
a
-
b
)
4.
If the expression
25
y
2
-
70
y
+
d
is a perfect square, where d is a constant, find the value of d
5.
Factorize
2
x
2
y
2
-
5
x
y
-
12
6.
Factorize completely
28
x
2
+
3
x
-
1
7.
Simplify
2
x
-
2
6
x
2
-
x
-
12
÷
x
-
1
2
x
-
3
8.
Simplify completely
3
x
2
-
1
x
2
-
1
-
2
x
+
1
x
+
1
9.
Factorize completely
3
x
2
-
2
x
y
-
y
2
10.
Find the greatest common factor of
x
3
y
3
and
4
x
y
4
. Hence factorize completely the expression
x
3
y
2
-
4
x
y
4
11.
Factorize
a
2
-
b
2
Hence find the exact value of
2557
2
-
2547
2
12.
Simplify the expression
5
a
-
4
b
=
2
[
a
-
(
2
b
+
c
)
]
13.
Simplify the expression
3
a
2
+
4
a
b
+
b
2
4
a
2
+
3
a
b
-
b
2
14.
Simplify the expression
3
x
2
-
4
x
y
+
y
2
9
x
2
-
y
2
15.
Simplify:
(
x
+
2
y
)
2
-
(
x
-
2
y
)
2
16.
Simplify the expression
4
x
2
+
y
2
2
x
2
-
7
x
y
+
3
y
2
17.
Simplify the expression
(
a
+
1
b
)
2
-
(
a
-
1
b
)
2
18.
Simplify the expression:
2
a
2
-
3
a
b
-
2
b
2
4
a
2
-
b
2
19.
Simplify the expression
9
t
2
-
25
a
2
6
t
2
+
19
a
t
+
15
a
2
20.
Simplify
p
2
+
2
p
q
+
q
2
p
3
-
p
q
2
+
p
2
q
-
q
3
21.
Expand the expression;
(
x
2
-
y
2
)
(
x
2
+
y
2
)
(
x
4
-
y
4
)
22.
Simplify the expression:
15
a
2
b
-
10
a
b
2
3
a
2
-
5
a
b
+
2
b
2
23.
Simplify the expression
a
4
-
b
4
a
3
-
a
b
2
24.
Simply the expression
12
x
2
+
a
x
-
6
a
2
9
x
2
-
4
a
2
25.
Simplify the expression
x
2
+
x
-
4
x
y
-
4
y
(
x
+
1
)
(
4
y
2
-
x
y
)
26.
Simplify the expression:
4
x
-
9
x
3
3
x
2
-
4
x
-
4
27.
Factorize
2
x
2
y
2
-
5
x
y
-
12
28.
Expand and simplify the expression
(
2
x
2
-
3
y
3
)
2
+
12
x
2
y
3
29.
Simplify the expression:
16
m
2
-
9
n
2
4
m
2
-
m
n
-
3
n
2
30.
Expand and simplify
(
x
+
2
y
)
2
-
(
2
y
-
3
)
2
31.
Simplify
p
2
+
2
p
q
+
q
2
p
3
-
p
q
2
+
p
2
q
-
q
3
32.
Expand and simplify
(
2
x
+
1
)
2
+
(
x
-
1
)
(
x
-
3
)
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