Question

1. what is the value of the 5th term of the expansion $(2x - 4)^4$?

256
$-256$
$b^4$
$a^4$

Explanation:

Step1: Recall binomial term formula

For $(a+b)^n$, $k$-th term: $\binom{n}{k-1}a^{n-(k-1)}b^{k-1}$

Step2: Identify values for the problem

Here, $a=2x$, $b=-4$, $n=4$, $k=5$

Step3: Calculate binomial coefficient

$\binom{4}{5-1}=\binom{4}{4}=1$

Step4: Compute $a$ and $b$ components

$a^{4-(5-1)}=(2x)^{0}=1$, $b^{5-1}=(-4)^4=256$

Step5: Multiply all components

$1 \times 1 \times 256=256$

Answer:

256