Question

compute the coefficient of x^4 in (2x+5)^10 . you can use C(n,r) or P(n,r) notation together with powers or integers. do not distribute the product. ​

Answer 1

Answer:

1312500000

Step-by-step explanation:

Given :

To find the coefiicient of $x^4$ in the expansion of $(2x + 5)^{10}$

Solution :

We know that,

$T_{r+1} = nC_r \times x^{n-r} \times a^{r}$

Here, n - r = 4,. (given power of x is 4)

and n = 10 ,

⇒ 10 - r = 4 ⇒ r = 6

⇒ $T_{6+1} = 10C_4 \times (2x)^4(5)^6$

⇒ $T_{6+1} = [10C_4 \times (2)^4(5)^6]x^4$

⇒ $[\frac{10!}{4!(10-4)!} \times 16 (390625)]x^4$

⇒ $[\frac{10 \times 9 \times 8 \times 7 \times 6!}{6! \times 4!} \times 6250000] x^4$

⇒ $[210 \times 6250000] x^4$

⇒ $1312500000 x^4$

∴ Coefficient of $x^4$  is 1312500000 (or) $10C4 (2)^4(5)^6$