Use the binomial theorem to expand the expression.
-$( x + 5 ) ^ { 4 }$
A) $x ^ { 4 } + 20 x ^ { 3 } + 150 x ^ { 2 } + 20 x + 625$
B) $x ^ { 4 } + 5 x ^ { 3 } + 150 x ^ { 2 } + 250 x + 625$
C) $x ^ { 4 } + 20 x ^ { 3 } + 150 x ^ { 2 } + 500 x + 625$
D) $x ^ { 4 } + 20 x ^ { 3 } + 250 x ^ { 2 } + 500 x + 625$

Question

Quizplus · Accepted Answer

The binomial theorem states that $(x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k}y^k$. For $(x + 5)^4$, the expansion is $x^4 + 4(5)x^3 + 6(5^2)x^2 + 4(5^3)x + 5^4$, which simplifies to $x^4 + 20x^3 + 150x^2 + 500x + 625$.

Use the Binomial Theorem to Expand the Expression (x+5)4( x + 5 ) ^ { 4 }(x+5)4

Use the Binomial Theorem to Expand the Expression $( x + 5 ) ^ { 4 }$