Equivalent expressions give the same value for every input. When a number sits outside parentheses, multiply it by every term inside, keeping each sign. Graph the original expression in Desmos, distribute by hand, then graph your rewrite to check that the lines overlap. Watch for the tempting mistake of turning a negative term positive.
Hints
- Hint 1
Graph the given expression as . An equivalent expression must give the same output for every input, so your rewrite should trace the entire line, not merely cross it once.
- Hint 2
The distributive property says the number outside parentheses multiplies each term inside. Treat as one negative term: what do you get when you multiply both and by ?
Step-by-step
Distribute, then check the graph
Step 1Graph the expression to match
Type in Desmos. It draws a line. Your rewrite must trace this entire line, since equivalent expressions agree for every .
- Step 2
Distribute to both terms
Use the distributive property: multiply the outside number by each term inside the parentheses, including its sign. Write both products: .
- Step 3
Multiply the two products
Multiply each product: . The constant stays negative because times is negative.
- Step 4
Check the matching line
Put the products together: . Add in Desmos. The two lines overlap throughout, confirming that the equivalent expression is . Choice D.