Expand the binomial by using the binomial theorem.
-$\left( 3 - y ^ { 3 } \right) ^ { 5 }$
A) $\left[ 3 + \left( - y ^ { 3 } \right) \right] ^ { 5 } ; 243 - 5 y ^ { 3 } + 10 y ^ { 6 } - 10 y ^ { 9 } + 5 y ^ { 12 } - y ^ { 15 }$
B) $\left[ 3 + \left( - y ^ { 3 } \right) \right] ^ { 5 } ; 243 - 405 y ^ { 3 } + 270 y ^ { 6 } - 90 y ^ { 9 } + 15 y ^ { 12 } - y ^ { 15 }$
C) $\left[ 3 + \left( - y ^ { 3 } \right) \right] ^ { 5 } ; 243 - 5 y + 10 y ^ { 2 } - 10 y ^ { 3 } + 5 y ^ { 4 } - y ^ { 6 }$
D) $\left[ 3 + \left( - y ^ { 3 } \right) \right] ^ { 5 } ; 243 - 405 y + 270 y ^ { 2 } - 90 y ^ { 3 } + 15 y ^ { 5 } - y ^ { 6 }$

Question

Quizplus · Accepted Answer

The binomial theorem states that $(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k$. Applying this to $(3 - y^3)^5$, we get the correct expansion as in option B, considering the coefficients calculated using the binomial coefficients for each term.

Expand the Binomial by Using the Binomial Theorem (3−y3)5\left( 3 - y ^ { 3 } \right) ^ { 5 }(3−y3)5

Expand the Binomial by Using the Binomial Theorem $\left( 3 - y ^ { 3 } \right) ^ { 5 }$