Question

what is the coefficient of the x^4 term in the expanded form of (2x-7)^6

Answer 1

Answer:

The coefficient of $x^{4}$ = 11760

Step-by-step explanation:

∵ The rule of expanded the binomial is :

$(a+b)^{n}=C_{0} ^{n} a^{n}b^{0}+C_{1}^{n}a^{n-1}b^{1}+C_{2}^{n}a^{n-2}b^{2}+.............$

∴ The Expanded of $(2x-7)^{6}$ is:

$(2x-7)^{6}=C_{0}^{6}(2x)^{6}(-7)^{0}+C_{1}^{6}(2x)^{5}(-7)^{1}+C_{2}^{6}(2x)^{4}(-7)^{2}+..........$

$(2x-7)^{6}=(1)(64x^{6})(1)+(6)(32x^{5})(-7)+(15)(16x^{4})(-7)^{2}$

We will take the term of $x^{4}$ and find the coefficient of it

∴ The coefficient of $x^{4}$ = $(15)(16)(-7)^{2}=(15)(16)(49)=11760$