Question

constant term in the expansion of (5x+2)^10​

Answer 1

Answer:

10 is the constant term ok

Answer 2

Answer:

Constant term in the expansion of $(5x+2)^{10}$ is 1024

Step-by-step explanation:

By  Binomial Theorem we have,

For any positive number 'n', and two real numbers 'a' and 'b'

$(a+b)^{n} = nC_0a^{n} + nC_1a^{n-1}b^{1} + nC_2a^{n-2}b^{2} + ............+nC_ra^{n-r}b^{r}+..........................+nC_nb^{n}, \\where nC_r = \frac{n!}{r! (n-r)!} and 0\leq r\leq n$

Substitute a = 5x  and b = 2  and n = 10 in the above equation we get,

$(5x+2)^{10} = 10C_0 (5x)^{10} + 10C_1 (5x)^{9} 2 + 10C_2 (5x)^{8} 2^2 +....................+10C_{10} 2^{10}$

By observing the above equation we can find that all the terms except the last term contains the variable the  'x'

So, the constant term is  $10C_{10} 2^{10}$ = $2^{10}$ = 1024  ( Since $10C_{10}$ = 1)

Hence the Constant term in the expansion of $(5x+2)^{10}$ is 1024.