Question 154·Easy·Equivalent Expressions
Which of the following expressions is equivalent to ?
For expression-equivalence questions, distribute carefully to remove parentheses, then combine like terms by separating variable terms from constants. Pay close attention to negative signs when subtracting a group, since changes both terms’ signs. Once simplified, match your result to the choices, and if time allows, plug in a simple value for the variable (like ) into both the original expression and a candidate choice to quickly confirm they are equal.
Hints
Start by expanding
First, expand each set of parentheses in by distributing the number outside the parentheses to both terms inside.
Be careful with the subtraction
Think of as adding a negative: you are distributing , not , to both and .
Combine like terms
After distributing, group the -terms together and the constant numbers together, then add or subtract them.
Desmos Guide
Type and expand the original expression
In Desmos, type 4(3y+2)-5(y-1) on one line. Desmos will show a simplified form next to the expression; compare that simplified expression to the answer choices.
Check by comparing with an option (optional)
To verify, you can also type the difference between the original expression and a choice, for example 4(3y+2)-5(y-1)-(7y+13). If Desmos simplifies this difference to 0 for all , then that choice matches the original expression.
Step-by-step Explanation
Distribute in the first term
Start with the expression:
Distribute the to both and :
So the whole expression becomes:
Distribute in the second term (watch the minus sign)
Now distribute the to both and in :
Substitute this back into the expression:
Combine like terms
Group the -terms and constant terms:
- and are like terms.
- and are constants.
Compute each group:
So the simplified expression is:
which matches answer choice A.