Question

Any genius in brainly ?

Solve :

Find the 4 th term of (x-3)^10

Answer 1

We have to find the 4 th term of  $(x-3)^{10}$

Binomial theorem :

$( x+y)^n=_nC_0x^n+_{n-1}C_1x^{n-1}y+....._nC_3x^{n-3}y^3+_nC_4x^{n-4}y^4....._nC_ny^n$

We see that the 5 th term is : $_nC_3x^{n-3}y^3$

Put n = 10 :

$=\:>_{10}C_3x^{10-3}y^3$

$=\:>_{10}C_3x^7y^3$

Put y = -3

$=\:>_{10}C_3x^7(-3)^3$

We know that : $_nC_r=\frac{n!}{r!(n-r)!}$

This case :  $_{10}C_3=\frac{10!}{3!\times7!}$

$=\:>\frac{8\times9\times10}{1\times2\times3}$

$=\:>4\times3\times10$

$=\:>120$

Hence the 4 th term = $120\times x^7\times-27$

$=\:>-3240x^7$

$\underline{\underline{\mathfrak{ANSWER}}}$

$\boxed{\sf{-3240x^7}}$

Answer 2

Answer:

-3240x⁷

Step-by-step explanation:

We know that General term of the expansion (a + b)ⁿ is:

T(r + 1) = C(n,r)a^(n - r)b^r.

Here,

We need to find the fourth term i.e T₄ in the expansion of (x - 3)¹⁰.

Here, r = 3, a = x, b = -3, n = 10.

Now,

T₄ = C(10,3)(x)¹⁰ ⁻³(-3)³

    = [10!/3!(10 - 3)!] * x⁷ * -27

    = [10!/3!7!] * x⁷ * -27

    = [3628800/30240] * x⁷ * -27

    = 120 * -27 * x⁷

    = -3240 * x⁷

Hope it helps!