Expand the binomial.
-$$( 2 x + 1 ) ^ { 4 }$$
A) $16 x ^ { 4 } + 32 x ^ { 3 } + 24 x ^ { 2 } + 8 x + 1$
B) $16 x ^ { 3 } + 32 x ^ { 2 } + 24 x + 8$
C) $\left( 4 x ^ { 2 } + 2 x + 1 \right) ^ { 4 }$
D) $16 x ^ { 4 } + 32 x ^ { 3 } + 24 x ^ { 2 } + 8 x + 2$

Question

Quizplus · Accepted Answer

To expand $(2x + 1)^4$, we use the binomial theorem or Pascal's triangle. The coefficients for the expansion of a binomial to the fourth power are 1, 4, 6, 4, 1. Applying these to $(2x)^4, (2x)^3(1), (2x)^2(1)^2, (2x)(1)^3, (1)^4$, we get $16x^4 + 32x^3 + 24x^2 + 8x + 1$.

Expand the Binomial (2x+1)4( 2 x + 1 ) ^ { 4 }(2x+1)4

Expand the Binomial $( 2 x + 1 ) ^ { 4 }$