Question

multiple choice 1 point
use the binomial theorem to expand the expression $(2x - 4y)^3$. then find the 2nd term.
$ - 16x^2y$
$ - 48x^2y$
$ 8x^3$
$ 96xy^2$

Explanation:

Step1: Recall binomial term formula

The $k$-th term (starting at $k=1$) of $(a+b)^n$ is $\binom{n}{k-1}a^{n-(k-1)}b^{k-1}$. For the 2nd term, $k=2$, $n=3$, $a=2x$, $b=-4y$.

Step2: Calculate binomial coefficient

$\binom{3}{2-1} = \binom{3}{1} = 3$

Step3: Compute $a$ component

$a^{3-(2-1)} = (2x)^{2} = 4x^2$

Step4: Compute $b$ component

$b^{2-1} = (-4y)^{1} = -4y$

Step5: Multiply all components

$3 \times 4x^2 \times (-4y) = 12x^2 \times (-4y) = -48x^2y$

Answer:

B. $-48x^2 y$