Question 127·Easy·Equivalent Expressions
Which of the following expressions is equivalent to ?
For expression-equivalence questions, first use the distributive property to remove parentheses and then combine like terms (same variable, same exponent) carefully. Work step by step: distribute, rewrite the expression, and then add or subtract coefficients of like terms. If you’re unsure, you can also plug in a simple value for (like or ) into the original expression and each answer choice; the correct choice will give the same value as the original for any value you test.
Hints
Start by removing parentheses
Focus on the part . How can you rewrite this without parentheses using the distributive property?
Distribute carefully
Multiply by each term inside the parentheses: first by , then by . Write down both resulting terms.
Combine like terms
After distributing, you will have two -terms: one from the distribution and one from . Add these like terms together.
Desmos Guide
Enter the original expression
In Desmos, type y = 4x(x - 7) + 3x to graph the original expression.
Enter each answer choice as a separate function
Add these functions:
y = 4x^2 - 31xy = 4x^2 - 25xy = 4x^2 - 28x + 3y = 7x^2 - 25x
Compare the graphs
Look at which option’s graph lies exactly on top of (coincides with) the graph of y = 4x(x - 7) + 3x for all visible -values. That function represents the expression equivalent to the original.
Step-by-step Explanation
Distribute across
Start with the given expression:
Distribute to both terms inside the parentheses:
So becomes:
Now the whole expression is:
Combine like terms
Now combine the like terms and :
So the simplified expression is:
This matches answer choice B, so the equivalent expression is .