IPMAT Indore 2022 (SA) - The sum of the coefficients of all the terms in the expansion of (5 x-9)^4 is __________. | PYQs + Solutions

IPMAT Indore 2022

Modern Math

Binomial Theorem

Medium

The sum of the coefficients of all the terms in the expansion of $(5 x-9)^{4}$ is __________.

Entered answer:

✅ Correct Answer: 256

To find the sum of coefficients in any polynomial expansion, substitute

x = 1

Take the original expression:

(5x - 9)^4

Substitute

x = 1

(5(1) - 9)^4 = (5 - 9)^4 = (-4)^4

Calculate

(-4)^4

(-4)^4 = (-4) \times (-4) \times (-4) \times (-4) = 16 \times 16 = 256

When we expand

(5x - 9)^4

, we get:

ax^4 + bx^3 + cx^2 + dx + e

To find

a + b + c + d + e

, substitute

x = 1

a(1)^4 + b(1)^3 + c(1)^2 + d(1) + e = a + b + c + d + e

This method works for any polynomial and is much faster than full expansion.

\therefore

Sum of coefficients

= 256