Question

Find the first three terms in the expansion of (2+u)^5 in ascending powers of u

Answer 1

Answer:

U^5 + 10U^4 + 40U^3

Step-by-step explanation:

(u + 2) ^ 5  = u^5 + 5 .2.U^4 + 10.2^2U^3

Answer 2

First three terms  are 32, 80u , 80u²

Step-by-step explanation:

To find the first 3 terms of $(2+u)^5$

As we know by binomial expansion of $(a+b)^n$ is given by $T_n=T_{r+1}= ^nC_r a^{n-r}b^r$  

First term of the expansion is

$T_1=T_{0+1}= \text{ } ^5C_0 2^{5-0}u^0= 1\times 2^5\times 1= 32$                 $\because \text{ } ^nC_0=1$

$T_2=T_{1+1}= \text{ }^5C_1 2^{5-1}u^1= 5\times 2^4\times u= 80u$               $\because \text{ } ^nC_1=n$

$T_3=T_{2+1}=\text{ } ^5C_2 2^{5-2}u^2= 10 \times 2^3\times u^2= 80u^2$              $\because \text{ } ^5C_2=\dfrac{5!}{2!(5-2)!} =\dfrac{5\times 4\times 3!}{2!\times 3!}=10$

Hence , First three terms  are 32, 80u , 80u²

#Learn more

1. Find the 7th term of(3x^2 - 1/3)^10​

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