Use the binomial formula to expand the binomial.
-$( \mathrm { w } - \mathrm { s } ) ^ { 6 }$
A) $w ^ { 6 } - 6 w ^ { 5 } s + 15 w ^ { 4 } s ^ { 2 } - 20 w ^ { 3 } s ^ { 3 } + 15 w ^ { 2 } s ^ { 4 } - 6 w s ^ { 5 } + s ^ { 6 }$
B) $w ^ { 6 } - s ^ { 6 }$
C) $w ^ { 6 } - 8 w ^ { 5 } s + 17 w ^ { 4 } s ^ { 2 } - 22 w ^ { 3 } s ^ { 3 } + 17 w ^ { 2 } s ^ { 4 } - 8 w s ^ { 5 } + s ^ { 6 }$
D) $w ^ { 6 } - 6 w ^ { 5 } s - 30 w ^ { 4 } s ^ { 2 } + 120 w ^ { 3 } s ^ { 3 } + 360 w ^ { 2 } s ^ { 4 } - 720 w s ^ { 5 } - 720 s ^ { 6 }$

Question

Quizplus · Accepted Answer

The binomial formula for the expansion of $(a - b)^n$ involves terms of the form $\binom{n}{k} a^{n-k} b^k$, where $\binom{n}{k}$ are the binomial coefficients. For $(w - s)^6$, the correct expansion involves calculating these coefficients correctly, which results in the sequence 1, 6, 15, 20, 15, 6, 1 for the powers of 6 down to 0, matching option A.

Use the Binomial Formula to Expand the Binomial (w−s)6( \mathrm { w } - \mathrm { s } ) ^ { 6 }(w−s)6

Use the Binomial Formula to Expand the Binomial $( \mathrm { w } - \mathrm { s } ) ^ { 6 }$