Which expression is equivalent to ?
For “Which expression is equivalent?” questions, either factor or distribute quickly. If the original expression is like , look for a greatest common factor and factor it out carefully, keeping track of signs. As a check, or if factoring feels unclear, distribute each answer choice back out in your head: only the correct choice will expand to exactly the original expression, with the same coefficients and signs.
Hints
Think about common factors
Look at the numbers 5 and 15 in . What is the largest number that divides both of them evenly?
Rewrite each term as a product
Try writing each term as and . Then think about how you could factor out the 5.
Check by distributing
For each answer choice, distribute the 5 (or 15) back in and see which one gives you exactly again.
Desmos Guide
Enter the original expression
In Desmos, type y = 5x - 15 on the first line to graph the original expression.
Enter each answer choice as a separate function
On the next lines, type y = 5(x - 3), y = 5(x + 3), y = 15(x - 5), and y = 5x(-3) so you have four more lines, one for each option.
Compare the graphs
Look for which option’s graph lies exactly on top of the graph of y = 5x - 15 for all x-values (they will appear as a single line when they match). That option is equivalent to the original expression.
Step-by-step Explanation
Look for a greatest common factor
The terms in are and . Ask: what number divides both 5 and 15? The greatest common factor (GCF) is 5, so we can factor 5 out of the expression.
Find what goes inside the parentheses
To factor out 5, divide each term by 5:
So, after taking 5 out, the expression inside the parentheses is .
Write the factored expression and match the choice
Putting it together, factoring out 5 gives
Now look at the answer choices and see that this matches choice A, .