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2. Chapter 1
Binomial Expansion
Subtopic
Construct Binomial Expansion by
using Pascal Triangle

3. *OBJECTIVE
At the end of the lesson,
you will be able to construct Binomial
Expansion by using Pascal Triangle

4. Pascal Triangle
n=positive only
(a  b) n  a nb0  a n1 b1  a n2 b2  a n3 b3  .......

6. 1
1
1
1
1
1
3
3
6
10
1
4
10
5
2 terms
T3
1
1 term
T2
1
2
4
5
T1
3 terms
T4
T5
1
1 T6
4 terms
PASCAL TRIANGLE
5 terms
6 terms

7.  p  2q 
1
4
a
1
n
1
b
1
1
Expand the expression by using Pascal Triangle.
1
2
3
4
1
3
6
1
4
1
( p  2q) 4  a nb0  a n1 b  a n2 b2  a n3 b3  a n4 b4
( p  2q) 4   p   2q    p   2q    p   2q    p   2q    p   2q 
4
0
3
1
1
2
2
3
2
1
3
4
( p  2q) 4   p 4 1   p3  2q    p 2 4q 2    p  8q3   116q 4 
( p  2q) 4  p 4  2 p3q  4 p 2 q 2  8 pq3  16q 4
1
4
6
4
1
( p  2q) 4  p 4  8 p3q  24 p 2 q 2  32 pq3  16q 4
0
5
4

8. m

 2  
4

1
3
1
n
1
b
a
1
2
3
Expand the expression by using Pascal Triangle.
(2 
m 3
)  a nb 0  a n 1 b  a n 2 b 2  a n 3 b3
4
0
1
2
m
3 m 
2 m 
1 m 
0 m 
(2  )3   2     2     2     2  
4
4
4
4
4
1
2
3
 m2 
 m3 
m 3
m
(2  )   81  4    2
 16   1 64 

 
4
4


 
1
(2 
3
3
m 3
3
1
)  8  3m  m 2  m3
4
8
64
1
4
1
3
1
3
1

9. EXERCISE
Expand all the questions below by using Pascal Triangle.
1
2  x 
6
 2 1
x  
x

2
2  x 11
7

3
 p  2q 5
8
3x  26
11
4
 x 2
  
2 x
5
(2 x  3 y ) 4
5
9
10
2y

7
1
 1

3
 a  b3 




x
1
e
5
4

x 5

10. 
Binomial Expansion when
the power positive