Select the correct answer.

Which expression is equivalent to [tex]$21 \sqrt[3]{15}-9 \sqrt[3]{15}$[/tex]?

A. 12
B. [tex]$30 \sqrt[3]{15}$[/tex]
C. [tex][tex]$12 \sqrt[3]{5}$[/tex][/tex]
D. [tex]$12 \sqrt[3]{15}$[/tex]



Answer :

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]