An equivalent expression gives the same value for every input. For a short expression with parentheses, distribute the outside number to every term, then combine terms with the same variable. Desmos can check the constant by graphing the original and reading where it crosses the vertical axis. The main trap is multiplying the variable term but leaving the constant untouched.
Hints
- Hint 1
The distributive property means the multiplies both terms inside the parentheses. Work out and separately before you do anything with the outside.
- Hint 2
On a graph, the vertical-axis crossing occurs when the input is . At that input, every variable term disappears. What constant should your rewritten expression have?
- Hint 3
The terms and are like terms: they have the same variable part, . Add their number parts, but keep the term with no separate.
Step-by-step
Distribute and combine
Step 1Multiply both terms inside the parentheses
Use the distributive property: the multiplies and , while the stays outside: .The outside reaches the negative term too.
- Step 2
Check the constant in Desmos
Type in Desmos, changing the problem's to so Desmos can graph it. Click the vertical-axis crossing, . At , the terms containing vanish, so this checks the constant term, .
- Step 3
Combine the terms with
Combine like terms, which have the same variable part; and combine, but stays separate: .So the equivalent expression is . Choice D.