Use the binomial theorem to expand the binomial. $$( z + t ) ^ { 3 }$$
A) $\quad z ^ { 3 } + 3 z ^ { 2 } t + 3 z t ^ { 2 } + t ^ { 3 }$
B) $\quad z ^ { 3 } + z ^ { 2 } t + z t ^ { 2 } + t ^ { 3 }$
C) $\quad z ^ { 3 } + t ^ { 3 }$
D) $\quad z ^ { 3 } + 2 z ^ { 2 } t + 2 z t ^ { 2 } + t ^ { 3 }$
E) none of the above

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 $(z + t)^3$, we get $z^3 + 3z^2t + 3zt^2 + t^3$, which matches option A.

Use the Binomial Theorem to Expand the Binomial (z+t)3( z + t ) ^ { 3 }(z+t)3

Use the Binomial Theorem to Expand the Binomial $( z + t ) ^ { 3 }$