Which of the following expressions is equivalent to the difference of and ?
For "equivalent expression" questions with words like sum, difference, product, or quotient, first translate the phrase into a symbolic expression using parentheses to keep each piece clear. Pay close attention to order words like "difference of A and B" (which means ), then carefully distribute any minus signs across parentheses before combining like terms. Doing this step-by-step—write, distribute, then combine—helps you avoid common sign errors and quickly match your result to the correct answer choice.
Hints
Understand the word "difference"
Ask yourself: when a problem says "the difference of A and B," which operation does that mean, and in what order should you write A and B?
Write the subtraction with parentheses
Rewrite the phrase as one expression with a minus sign: put each polynomial in parentheses so you can see clearly what is being subtracted.
Handle the minus sign carefully
When you subtract the second polynomial, think about how the minus sign affects each term inside the second parentheses before you combine like terms.
Combine like terms
After distributing the minus sign, group together the terms, the terms, and the constant terms and then simplify each group.
Desmos Guide
Use Desmos to simplify the expression
In a Desmos expression line, type
and press Enter. Desmos will show the simplified polynomial form of this expression; compare that simplified expression to the answer choices to see which one matches.
Step-by-step Explanation
Translate the word phrase into an algebraic expression
"The difference of and " means you subtract the second expression from the first.
So write it as
The order is important: first expression minus second expression.
Distribute the minus sign and group like terms
To subtract the second polynomial, distribute the negative sign across every term inside the second parentheses.
Now group like terms (the terms together, the terms together, and the constants together):
Simplify the grouped terms to find the equivalent expression
Now simplify each group:
So the whole expression becomes
This matches choice B.