Find a Particular Term in a Binomial Expansion
-$( x - 3 ) ^ { 17 }$
A) $x^{ 17} - 51 x^{ 16} + 1224 x^{ 15}$
B) $x ^ { 17 } - 51 x^{ 16} - 1224 x^{ 15}$
C) $x^{ 17} + 51 x^{ 16} + 1224 x^{ 15}$
D) $x ^{ 17} + 51 x^{ 16} - 1224 x^{ 15 }$

Question

Find a Particular Term in a Binomial Expansion
-$( x - 3 ) ^ { 17 }$
A) $x^{ 17} - 51 x^{ 16} + 1224 x^{ 15}$
B) $x ^ { 17 } - 51 x^{ 16} - 1224  x^{ 15}$
C) $x^{ 17} + 51 x^{ 16} + 1224  x^{ 15}$
D) $x ^{ 17} + 51 x^{ 16} - 1224 x^{ 15 }$

Quizplus · Accepted Answer

The correct expansion for the given binomial expression $(x - 3)^{17}$ starts with $x^{17}$, and the coefficients of the subsequent terms can be calculated using the binomial theorem. The coefficient of $x^{16}$ is $-51$ because it is $17$ (from $17C1$) multiplied by $-3$ (the second term of the binomial raised to the first power). Similarly, the coefficient of $x^{15}$ is $1224$, calculated from $17C2$ times $(-3)^2$, which gives a positive value. Thus, option A correctly represents the first three terms of the expansion.

Find a Particular Term in a Binomial Expansion - (x−3)17( x - 3 ) ^ { 17 }(x−3)17

Find a Particular Term in a Binomial Expansion
- $( x - 3 ) ^ { 17 }$