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Vikki [24]
2 years ago
12

Find the first three terms in the expansion , in ascending power of x , of (2+x)^6 and obtain the coefficient of x^2 in the expa

nsion of (2+x-x^2)^6
please answer quickly​
Mathematics
1 answer:
Nataly_w [17]2 years ago
3 0

Answer:

The first 3 terms in the expansion of (2 + x)^{6} , in ascending power of x are,

64 , 192 \times x^{1} {\textrm{  and  }}240 \times x^{2}

coefficient of x^{2} in the expansion of (2+x - x^{2})^{6} = (240 - 192) = 48

Step-by-step explanation:

(2+x)^{6}

= \sum_{k=0}^{6}(6_{C_{k}} \times x^{k} \times 2^{6 - k})

= 6_{C_{0}} \times x^{0} \times 2^{6}  + 6_{C_{1}} \times x^{1} \times 2^{5} + 6_{C_{2}} \times x^{2} \times 2^{4} + terms involving higher powers of x

= 64 + 192 \times x^{1} + 240 \times x^{2} + terms involving higher powers of x

so, the first 3 terms in the expansion of (2 + x)^{6} , in ascending power of x are,

64 , 192 \times x^{1} {\textrm{  and  }}240 \times x^{2}

Again,

(2+x - x^{2})^{6}

= \sum_{k=0}^{6}(6_{C_{k}} \times (2 + x)^{k} \times (-x^{2})^{6 - k})

Now, by inspection,

the term x^{2} comes from k =5 and k = 6

for k = 5, the coefficient of  x^{2}  is , (-32) \times 6 = -192

for k = 6 , the coefficient of x^{2} is, 6_{C_{2}} \times 2^{4} = 240

so,   coefficient of x^{2} in the final expression = (240 - 192) = 48

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Read 2 more answers
Brand X sells 21 oz. Bags of mixed nuts that contain 29% peanuts. To make their product they combine brand A mixed nuts which co
masha68 [24]

Answer:

Brand X has to mix 8.4 oz of brand A mixed nuts which contain 35% peanuts and 12.6 oz of brand B mixed nuts which contain 25%, to obtain 21 oz. Bags of mixed nuts that contain 29% peanuts.

Step-by-step explanation:

Hi

We define

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B_{B}=1oz @ 25\%, wich means Brand b has 1 oz containing 25% peanuts.

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Jenna can clean the gutters at her house in four hours. Her older brother, John, can clean the gutters in three hours, if they w
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Answer:

1 hour and 42.8 minutes

Step-by-step explanation:

To answer this question let's call t_1 while it takes Jenna to clean the gutters

Let's call t_2 while it takes John to clean the gutters

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