which is the third term of the expansion(x^2 - x)^20?(a)190x^38 (b)-190x^39 (c)1140x^38 (d)-1140x^38?

Question

third term expansion is a type of mathametical solution in algebra

Answer 1

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Answer 2

1- The first three terms, when expanded, have the following powers:

First term: (x^2)^20
Second Term: -A[(x^2)^19]x
Third Term: B[(x^2)^18]x^2

Where A & B are unknown coefficients.

Now, we know the power of x in the third term is 38

2- To know the coefficient of the third term (B), just look at the triangle of coefficients known as Pascal triangle. There you can see the coefficient is 190.


Considering (1) & (2) 190x^38 is the right answer. Select (a)!

Answer 3

The rth term of the binomial expansion (a + b)^n is
nC(r - 1) a^(n - r + 1) b^(r - 1)

Since the binomial is
(x² - x)^20,
you can simplify it first by removing the common monomial x
= [x(x - 1)]^20
= x^20(x - 1)^20

Thus, the 3rd term is
= x^20 · 20C(3 - 1) x^(20 - 3 + 1) (-1)^(3 - 1)
= x^20 · 20C2 x^(18) · (-1)^(2)
= x^20 · 20!/(20 - 2)!2! x^18 · 1
= x^20 · 190 · x^18
= 190 x^38

Therefore, the correct choice is (a)

^_^

Answer 4

Using combinations
20C2 [(x^2)^20-2] [(-1)^2] (x^2)

This solves to 190x^38.
So answer is (a)

Answer 5

2nd term is to the power of 40. Thus 3rd term is either (a), (c) or (d)
To get x^38, needs multiply 18 of 'x^2' and 2 of 'x'. Thus, the term is positive.
Number of ways to obtain power of 38 is 20C2 = 20x19/2! = 190. Thus (a) is the answer.

Answer 6

its (a)190x^38

in binomial series any (m+1) no. term of (a+x)^n will be

nCm*a^(n-m)*x^m

for the case, n=20, m=2

so, the result will be 20C2*(x^2)^18*(-x)^2=190x^38

Answer 7

ANS : 190x^38

www.quickmath.com will expand it for you.

Answer 8

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Answer 9

mine is (a)