Question 46·Easy·Equivalent Expressions
The expression
is given.
Which of the following expressions is equivalent to the given expression?
For expression-equivalence questions like this, use the distributive property carefully: multiply the number outside the parentheses by each term inside, paying special attention to negative signs. Simplify the result and then match it directly to the answer choices. If you’re unsure, you can also plug in a simple value for (like ) into the original expression and each option; any choice that doesn’t give the same value as the original can be eliminated.
Hints
Think about the property involved
What property tells you how to multiply a number outside parentheses by each term inside the parentheses?
Apply the property step by step
Take and multiply by , then multiply by . Write both results out separately.
Watch the sign on the constant term
When you multiply by , should the result be positive or negative? Use that to decide the correct sign in your final expression.
Desmos Guide
Enter the original expression as a function
In Desmos, type y = 4(2x - 3) to represent the given expression as a graph.
Enter each answer choice as its own function
Type four more lines: y = 8x + 12, y = 8x - 15, y = 8x + 15, and y = 8x - 12. Each will show as a different line on the graph.
Compare the graphs to find the equivalent expression
Look for the line that lies exactly on top of the graph of y = 4(2x - 3) for all values of . The expression that produces that overlapping line is the one equivalent to the original.
Step-by-step Explanation
Recall the distributive property
The distributive property says that for any numbers , , and ,
and it also works with subtraction:
Here, the number outside the parentheses is and the expression inside is .
Distribute 4 to each term in the parentheses
Multiply by each term inside :
- First term:
- Second term:
Be careful with the sign on ; multiplying a positive number by a negative number gives a negative result.
Combine the distributed terms into a single expression
Put the two results together:
So the expression equivalent to is , which matches choice D.