Select the correct answer.
Which expression is equivalent to $21 \sqrt[3]{15}-9 \sqrt[3]{15}$ ?
A. 12
B. $30 \sqrt[3]{15}$
C. $12 \sqrt[3]{5}$
D. $12 \sqrt[3]{15}$
Answer (1)
Identify the common term: Both terms have the same cube root, 3 15 .
Factor out the common term: 21 3 15 − 9 3 15 = ( 21 − 9 ) 3 15 .
Perform the subtraction: 21 − 9 = 12 .
The simplified expression is: 12 3 15 .
Explanation
Understanding the problem We are asked to simplify the expression 21 3 15 − 9 3 15 . Both terms contain the same cube root, which is 3 15 . This means we can combine these terms by subtracting their coefficients.
Factoring out the common term To simplify the expression, we factor out the common term 3 15 :
21 3 15 − 9 3 15 = ( 21 − 9 ) 3 15
Performing the subtraction Now, we perform the subtraction within the parentheses:
21 − 9 = 12
Substituting the result Substitute the result back into the expression:
( 21 − 9 ) 3 15 = 12 3 15
Final Answer Therefore, the simplified expression is 12 3 15 . Comparing this to the given options, we see that it matches option D.
Examples
Imagine you're baking and a recipe calls for 21 scoops of a special spice blend, but you only need 9 scoops. The expression 21 3 15 − 9 3 15 is like figuring out how many scoops you'll actually use. By simplifying it to 12 3 15 , you find out you only need 12 scoops of the special spice blend, making your baking preparations easier and more accurate. This kind of simplification is useful in many real-life situations where you need to combine or reduce quantities.
