Expand the expression using the Binomial Theorem.
-$$( x + 1 ) ^ { 6 }$$
A) $x ^ { 6 } + 6 x ^ { 5 } + 15 x ^ { 4 } + 20 x ^ { 3 } + 15 x ^ { 2 } + 6 x + 6$
B) $x ^ { 6 } + 6 x ^ { 5 } + 15 x ^ { 4 } + 20 x ^ { 3 } + 15 x ^ { 2 } + 6 x + 1$
C) $x ^ { 6 } + 6 x ^ { 5 } + 30 x ^ { 4 } + 120 x ^ { 3 } + 30 x ^ { 2 } + 6 x + 1$
D) $x ^ { 6 } + 6 x ^ { 5 } + 30 x ^ { 4 } + 120 x ^ { 3 } + 360 x ^ { 2 } + 720 x + 720$

Question

Quizplus · Accepted Answer

The Binomial Theorem states that $(x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k}y^k$. Applying this to $(x + 1)^6$, the coefficients are determined by the binomial coefficients $\binom{6}{k}$, leading to the expansion $x^6 + 6x^5 + 15x^4 + 20x^3 + 15x^2 + 6x + 1$, which matches option B.

Expand the Expression Using the Binomial Theorem (x+1)6( x + 1 ) ^ { 6 }(x+1)6

Expand the Expression Using the Binomial Theorem $( x + 1 ) ^ { 6 }$