Find the product of \( (-d+e)(4 e+d) \). Which statements are true? Check all that apply. There are 2 terms in the product. There are 3 terms in the product. There are 4 terms in the product. The product is degree 1 . The product is degree 2 . The product is degree 4 .

Simplify the expression by following steps: - step0: Multiply the terms: \(\left(-d+e\right)\left(4e+d\right)\) - step1: Apply the distributive property: \(-d\times 4e-d\times d+e\times 4e+ed\) - step2: Reorder the terms: \(-4ed-d^{2}+4e^{2}+ed\) - step3: Add the terms: \(-3ed-d^{2}+4e^{2}\) Let's find the product of \( (-d+e)(4e+d) \). 1. **Expand the expression**: \[ (-d+e)(4e+d) = -d \cdot 4e + -d \cdot d + e \cdot 4e + e \cdot d \] This simplifies to: \[ -4de - d^2 + 4e^2 + ed \] Combining like terms gives: \[ -3de - d^2 + 4e^2 \] 2. **Count the terms**: The expanded expression is: \[ -3de - d^2 + 4e^2 \] This has **3 distinct terms**: \(-3de\), \(-d^2\), and \(4e^2\). 3. **Determine the degree**: - The degree of a term is the sum of the exponents of the variables in that term. - The term \(-3de\) has a degree of \(1 + 1 = 2\). - The term \(-d^2\) has a degree of \(2\). - The term \(4e^2\) has a degree of \(2\). - Therefore, the highest degree among the terms is \(2\). Now, let's evaluate the statements: - **There are 2 terms in the product.** (False) - **There are 3 terms in the product.** (True) - **There are 4 terms in the product.** (False) - **The product is degree 1.** (False) - **The product is degree 2.** (True) - **The product is degree 4.** (False) ### True Statements: - There are 3 terms in the product. - The product is degree 2.