Expand the binomial by using the binomial theorem.
-$$( 5 y + 1 ) ^ { 4 }$$
A) $625 y ^ { 4 } + 1$
B) $625 y ^ { 4 } + 500 y ^ { 3 } + 150 y ^ { 2 } + 20 y + 1$
C) $625 y ^ { 4 } + 500 y ^ { 3 } + 200 y ^ { 2 } + 20 y + 1$
D) $625 y ^ { 4 } + 20 y ^ { 3 } + 150 y ^ { 2 } + 500 y + 1$

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 $(5y + 1)^4$, we calculate each term: $\binom{4}{0}(5y)^4(1)^0 = 625y^4$, $\binom{4}{1}(5y)^3(1)^1 = 500y^3$, $\binom{4}{2}(5y)^2(1)^2 = 150y^2$, $\binom{4}{3}(5y)^1(1)^3 = 20y$, and $\binom{4}{4}(5y)^0(1)^4 = 1$, leading to the expansion $625y^4 + 500y^3 + 150y^2 + 20y + 1$.

Expand the Binomial by Using the Binomial Theorem (5y+1)4( 5 y + 1 ) ^ { 4 }(5y+1)4

Expand the Binomial by Using the Binomial Theorem $( 5 y + 1 ) ^ { 4 }$