Question

Explain the difference between the phrases “4 times the sum ofx and y” and “the sum of 4 times x and y”.

Short answer

• The resultant expression for the phrase "4 times the sum ofx and y"is $4\left(x+y\right)$.
• The resultant expression for the phrase "the sum of 4 times xand y"is$4x+y$.

Step-by-step solution

Step 1. Given Information

The given phrase are "“4 times the sum ofx and y” and “the sum of 4 times xand y”.

Step 2. Write the algebraic expression for the phrase "4 times the sum of x and y."

• The keyword "times and "sum" shows the operation of multiplication and the operation of addition respectively.
• After observing the word "of" and "and", there are two numbers, xand y ,and they are added. Multiply the sum by 4.

$4\left(x+y\right)$

Step 3. Write the algebraic expression for the phrase "the sum of 4 times x and y”.

• Follow the previous step, there are two numbers, which are "4 times xor 4x"and"y".
• The number4x added to y.

$4x+y$

Step 4. Conclusion.

The results of both phrases are different.

• The resultant expression for the phrase "4 times the sum ofx and y"is $4\left(x+y\right)$.
• The resultant expression for the phrase "the sum of 4 times xand y"is $4x+y$.