Use the binomial formula to expand the binomial.
-$( x - 1 ) ^ { 6 }$
A) $x ^ { 6 } - 6 x ^ { 5 } - 30 x ^ { 4 } - 120 x ^ { 3 } - 360 x ^ { 2 } - 720 x + 720$
B) $x ^ { 6 } - 6 x ^ { 5 } - 15 x ^ { 4 } - 20 x ^ { 3 } - 15 x ^ { 2 } - 6 x - 6$
C) $x ^ { 6 } - 6 x ^ { 5 } + 30 x ^ { 4 } - 120 x ^ { 3 } + 30 x ^ { 2 } - 6 x + 1$
D) $x ^ { 6 } - 6 x ^ { 5 } + 15 x ^ { 4 } - 20 x ^ { 3 } + 15 x ^ { 2 } - 6 x + 1$

Question

Quizplus · Accepted Answer

The correct expansion using the binomial theorem for $(x - 1)^6$ results in alternating signs and coefficients determined by the binomial coefficients, which correctly matches option D.

Use the Binomial Formula to Expand the Binomial (x−1)6( x - 1 ) ^ { 6 }(x−1)6

Use the Binomial Formula to Expand the Binomial $( x - 1 ) ^ { 6 }$