3 years ago

(x-1)^7/2 - (x-1)^3/2 factor and simplify. Show step-by-step solution.

2 answers:

4 0

$(x-1)^{7/2} -(x-1) ^{3/2}= \\ =(x-1)^{3/2}*(x-1) ^{4/2}-(x-1) x^{3/2}= \\ =(x-1) ^{3/2}*((x-1) ^{2} - 1) = \\ =(x-1) ^{3/2}*(x-1+1)*(x-1-1) = \\ =x*(x-2)*(x-1) ^{3/2}$

telo118 [61]3 years ago

4 0

(x-1)^3/2((x-1)^2-1) =(x+1)(x-1)^5/2

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What is the second term in the binomial expansion of (2r – 3s)12? –73,728r11s 73,728r11s 608,256r10s2 –608,256r10s2?

ZanzabumX [31]

Solution:

A is the correct option.

Explanation:

We have been given that $(2r - 3s)^{12}$

The $r^{th}$ term of a binomial expansion $(a+b)^n$ is given by

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For the given binomial expansion, we have

$a=2r,b=-3s,r=2,n=12$

On plugging this value in the above formula, we have

$t_2=^{12}C_{2-1}(2r)^{12-2+1}(-3s)^{2-1}\\\\t_2=^{12}C_1 (2r)^{11}(-3s)^{1}\\\\t_2=\frac{12!}{1!11!}(2)^{11}r^{11}(-3)s\\\\t_2=12\cdot (2)^{11}(-3)r^{11}s\\\\t_2=-73728r^{11}s$

Therefore, the second term is -73728r^11 s

A is the correct option.

3 0

3 years ago

Read 2 more answers

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timama [110]

12/3 is already an improper fraction.

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telo118 [61]

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Step-by-step explanation:

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Step-by-step explanation:

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