Expand and write the coefficient of 'x' in the expansion of (x+4)3 .
Answers
Answer:
When a binomial is raised to whole number powers, the coefficients of the terms in the expansion form a pattern. These expressions exhibit many patterns: Each expansion has one more term than the power on the binomial. The sum of the exponents in each term in the expansion is the same as the power on the binomial.
Step-by-step explanation:
pls mark my answer as brainliest
Answer:
x)
5
.
HARD
Help best friend
Study later
ANSWER
First expand the term (1+2x)
4
by binomial expansion.
(1+2x)
4
=
4
C
0
(1)
4
(2x)
0
+
4
C
1
(1)
3
(2x)
1
+
4
C
2
(1)
2
(2x)
2
+
4
C
3
(1)
1
(2x)
3
+
4
C
4
(1)
0
(2x)
4
=1+8x+24x
2
+32x
3
+16x
4
(1)
Now expand the term (2−x)
5
by binomial expansion,
(2−x)
5
=
5
C
0
(2)
5
(x)
0
−
5
C
1
(2)
4
(x)
1
+
5
C
2
(2)
3
(x)
2
−
5
C
3
(2)
2
(x)
3
+
5
C
4
(2)
1
(x)
4
−
5
C
5
(2)
0
(x)
5
=32−80x+80x
2
−40x
3
+10x
4
−x
5
(2)
Multiply the coefficients of those powers which can give the term x
4
and then add from equation (1) and (2).
=1×10+8(−40)+24(80)+32(−80)+16(32)
=−438
Therefore, the coefficient of x
4
is −438.