Question

simplify the expression completely.
$c(4b^3 + 3a) + b(2cb^2 - 6ac)$
a $6cb^3 - 3abc$
b $6cb^3 + 3ac - 6abc$
c $4cb^3 + 3a + 2cb^3 - 6ac$
d $4b^3 + 3a + 2b^2 - 6ac$
e $c + 4b^3 + 3a + b + 2b^2 - 6ac$

Explanation:

Step1: Distribute the terms

First, distribute \( c \) in \( c(4b^3 + 3a) \): \( c\times4b^3 + c\times3a = 4cb^3 + 3ac \).
Then, distribute \( b \) in \( b(2cb^2 - 6ac) \): \( b\times2cb^2 - b\times6ac = 2cb^3 - 6abc \).

Step2: Combine like terms

Now, combine the two results: \( (4cb^3 + 3ac) + (2cb^3 - 6abc) \).
Combine the \( cb^3 \) terms: \( 4cb^3 + 2cb^3 = 6cb^3 \).
The other terms remain: \( 3ac - 6abc \).

So the simplified expression is \( 6cb^3 + 3ac - 6abc \).

Answer:

B. \( 6cb^3 + 3ac - 6abc \)