Sure, let's solve the given problem step-by-step.
Given the expression:
[tex]\[ 21 \sqrt[3]{15} - 9 \sqrt[3]{15} \][/tex]
Step 1: Identify like terms
Notice that both terms contain the cube root of 15 ([tex]\(\sqrt[3]{15}\)[/tex]).
Step 2: Factor out the common term
We can factor out the common term, [tex]\(\sqrt[3]{15}\)[/tex], from both parts of the expression:
[tex]\[ 21 \sqrt[3]{15} - 9 \sqrt[3]{15} = (21 - 9) \sqrt[3]{15} \][/tex]
Step 3: Simplify the coefficients
Subtract the coefficients:
[tex]\[ 21 - 9 = 12 \][/tex]
So, the expression simplifies to:
[tex]\[ 12 \sqrt[3]{15} \][/tex]
Thus, the expression equivalent to [tex]\(21 \sqrt[3]{15} - 9 \sqrt[3]{15}\)[/tex] is:
[tex]\[ 12 \sqrt[3]{15} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{12 \sqrt[3]{15}} \][/tex]
So, the correct option is:
D. [tex]\( 12 \sqrt[3]{15} \)[/tex]
