Skill: Translate algebraic expressions into words

To translate an algebraic expression into words:

1. Identify the parts inside grouping symbols first.
2. Name exponents precisely, such as “squared.”
3. Identify multiplication using words such as “times” or “the product of.”
4. Read addition and subtraction in the correct order.
5. Do not use an equals sign; you are describing an expression, not an equation.

Example: Translate

$$2(x+5)^2-3y$$

Step 1: Read the grouped part.

The parentheses contain $(x+5)$, so say:

“the sum of $x$ and $5$”

Step 2: Read the exponent.

The entire sum is raised to the second power, so say:

“the square of the sum of $x$ and $5$”

This is different from saying “$x$ plus $5$ squared,” which could suggest that only $5$ is squared.

Step 3: Read the coefficient.

The $2$ multiplies the squared expression, so say:

“twice the square of the sum of $x$ and $5$”

Step 4: Read the remaining term.

The $3$ is multiplied by $y$, so $(3y)$ is:

“three times $y$”

Step 5: Read the subtraction.

The expression subtracts $(3y)$ from the first part. A precise translation is:

“The difference between twice the square of the sum of $x$ and $5$ and three times $y$.”

The phrase “the difference between” shows that the second quantity is subtracted from the first.