use the formula to expand (p+5)^2
Answers
(p+5)²
=p²+25+10p.....
Answer:
Bavly · Stefan V.
Feb 10, 2016
The final answer :
(
a
+
b
)
5
=
a
5
+
5
.
a
4
.
b
+
10
.
a
3
.
b
2
+
10
.
a
2
.
b
3
+
5
.
a
1
.
b
4
+
b
5
Explanation:
The binomial theorem tells us that if we have a binomial (a+b) raised
to the
n
t
h
power the result will be
(
a
+
b
)
n
=
n
∑
k
=
0
c
n
k
⋅
a
n
−
k
⋅
b
n
where
c
n
k
=
n
!
k
!
(
n
−
k
)
!
and is read "n CHOOSE k equals n factorial divided by k factorial (n-k) factorial".
So
(
a
+
b
)
5
=
a
5
+
5
.
a
4
.
b
+
10
.
a
3
.
b
2
+
10
.
a
2
.
b
3
+
5
.
a
1
.
b
4
+
b
5
we notice that the powers of ' a ' keeps decreasing from 5 (which representes ' n ') until it reaches
a
zero
at the last term.
also we notice that the power of ' b ' keeps increasing from zero untill it reaches 5 at the last term.
Now the we have to determine the coefficient of each term through the...
c
n
k
=
n
!
k
!
(
n
−
k
)
!
first coefficient