Question

The sum of the coefficients of odd powers of x in (1+x-x2-x3) ²×³ is​

Answer 1

Answer:

Correct option is B

512

Sum of the coefficient of odd powers of x in f(x) is

2

f(1)+f(−1)

=

2

(1+1+1+1)

5

+(1−1+1−1)

5

=

2

4

5

=512

Answer 2

Question :-

• Find the sum of coefficients of odd powers of x in the expansion

Answer :-

• The sum of coeffients of odd powers of x is 8

Explanation:

Given :-

• Multinomial expression ( 1 + x - x² - x³)²

To Find :-

• The sum of the coefficients of odd powers of x

Using Formula :-

$\bigstar \; {\underline{\boxed{\bf{ Sum \; of \; odd \; coefficients = \frac{f(1) - f(-1)}{2} }}}}$

Required Solution:-

★ Now let's find out f(1) firstly

$\longrightarrow \sf f(x) = (1 + x-x^2 -x^3 )^2$

$\longrightarrow \sf f(1) = (1 + 1-1 - 1 )^2$

$\longrightarrow \sf f(1) = (0)^2 = 0$

★ Now let's find out f(-1)

$\longrightarrow \sf f(x) = (1 + x-x^2 -x^3 )^2$

$\longrightarrow \sf f(-1) = (1 + 1 + 1 + 1 )^2$

$\longrightarrow \sf f(-1) = (4)^2 = 2^4$

★ Now substituting it in the formula

$\longrightarrow \sf \dfrac{f(1) - f(-1)}{2}$

$\longrightarrow \sf \dfrac{0 - (2 )^4}{2}$

$\longrightarrow \sf \dfrac{2^4}{2}$

$\longrightarrow \sf 2^3$

$\longrightarrow \sf {\boxed{\underline{\pink \sf{ 8 }}}}$

Therefore:-

• The sum of the coefficients of odd powers is 8

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