Question 148·Easy·Equivalent Expressions
Which expression is equivalent to ?
For “equivalent expression” questions with sums of products, first scan for a common factor across all terms—often a shared binomial like . Factor that out before doing any FOIL, then simplify the smaller expression that remains inside the brackets. Finally, rewrite the product in a clean, standard order (constants, then , then binomials) and match it directly to the choice that has the same factored form; this is faster and less error-prone than fully expanding and then refactoring.
Hints
Look for a common factor
In the expression , what factor appears in both terms?
Factor before expanding
Instead of using FOIL on , try factoring the common binomial you found out of the entire expression.
Combine like terms inside the brackets
After you factor out the common binomial, you will have something like that binomial times a bracket. Carefully simplify the sum inside the bracket before comparing to the choices.
Desmos Guide
Enter the original expression
In Desmos, type y1 = (x+3)(2x-5) + 5(x+3) to represent the original expression.
Enter each answer choice as separate functions
Type:
y2 = (x+3)(2x-10)y3 = (2x-5)(x-5)y4 = 2x(x+3)y5 = 2(x+3)so each option is graphed as a separate function.
Compare graphs or tables
Either look at the graphs to see which -graph lies exactly on top of for all , or use a table (click the gear icon and “Table”) and compare the -values of to those of each option at several -values. The option whose function always matches is the equivalent expression.
Step-by-step Explanation
Notice the common factor
The expression is .
Both terms contain the factor , so you can factor out instead of multiplying everything out.
Factor out the common binomial
Write the expression as a product using the common factor:
Now the expression is a single product involving and a simpler bracket.
Simplify inside the brackets and match an answer choice
Simplify the part in brackets:
So the entire expression becomes
Rewriting the product in a more standard order gives , which matches answer choice C.