An equivalent expression has the same value for every . A factor outside parentheses calls for the distributive property: multiply every term inside before combining like terms. You can check your distribution in Desmos by graphing the original and expanded expressions; their curves should overlap completely. A negative factor changes every term, and multiplying two negatives makes a positive.
Hints
- Hint 1
The distributive property means the negative factor multiplies all three terms inside the parentheses. What happens when multiplies the middle term, ?
- Hint 2
Graph the original expression and your expanded expression as two equations in Desmos. Full overlap checks the distribution; curves that meet at only one point might still represent different expressions.
- Hint 3
Combine like terms: terms go with terms, and terms go with terms. Keep the constant term separate while you add each group's coefficients.
Step-by-step
Distribute, check, and combine
Step 1Distribute the negative factor
The factor outside the second parentheses is negative . By the distributive property, it multiplies every term inside; in particular, . Multiply all three terms:
- Step 2
Check the distribution in Desmos
Type and . Desmos draws overlapping curves across the window, so the distribution kept the signs consistent. A single meeting point wouldn't be enough to show that.
- Step 3
Combine like terms
Like terms have the same power of , so group the terms and the terms separately:
Add each group's coefficients:
The equivalent expression is . Choice D.