The same parentheses in two terms signal a common factor, a piece both terms share. Combine the numbers multiplying that shared piece before distributing. Then graph the original expression and your rewrite in Desmos to check that they overlap. Because the terms are subtracted, subtract their outside numbers rather than adding them.
Hints
- Hint 1
A common factor is a piece that multiplies both terms. Here, the whole parenthesis is shared. What happens if you keep it intact and subtract the two numbers outside it?
- Hint 2
The distributive property says to multiply the outside number by each term inside the parentheses. After combining the outside numbers, what sign will the constant have?
Step-by-step
Combine the shared factor
Step 1Keep the shared parentheses together
Both terms multiply the same , so use the distributive property backward to combine their outside numbers:
Subtract the outside numbers:
The is subtracted, not added.
- Step 2
Check the factored rewrite
Type and in Desmos. Their lines overlap, confirming that combining the shared factor preserves the expression.
- Step 3
Distribute to finish the rewrite
Multiply by both terms inside the parentheses:
The constant is negative because . So the expression is equivalent to . Choice D.