Question

Find the coefficient of the 6th term of the binomial expansion for (x + y)9841263654

Answer 1

The binomial expansion formula is given below;

$(a+b)^n=^nC_0a^nb^0+^nC_1a^{n-1}b^1+^nC_2a^{n-2}b^2+\ldots\ldots\ldots.^nC_na^0b^n$

To expand the question and comparing to the formula above, we have

$(x+y)^9=^9C_0x^9y^0+^9C_1x^8y^1+^9C_2x^7y^2+^9C_3x^6y^3+^9C_4x^5y^4+^9C_5x^4y^5+^9C_6x^3y^6+^9C_7x^2y^7+^9C_8x^1y^8+^9C_9x^0y^9$

Calculating the coefficients using combination formula;

$^nC_r=\frac{n!}{(n-r)!r!}$$(x+y)^9=1x^9y^0+9_{}x^8y^1+36x^7y^2+84x^6y^3+126_{}x^5y^4+126x^4y^5+84x^3y^6+36x^2y^7+9x^1y^8+1_{}x^0y^9$$(x+y)^9=x^9^{}+9_{}x^8y^{}+36x^7y^2+84x^6y^3+126_{}x^5y^4+126x^4y^5+84x^3y^6+36x^2y^7+9x^{}y^8+y^9$

From the solution, the 6th term is

$126x^4y^5$

Hence, the coefficient of