(1) \( x^{2}+7 x+10 \) (1) \( x^{2}+7 x-10 \) (4) \( x^{2}+5 x+b \) (D) \( 3 a b+6 b-3 a+2 b \) ()) \( 2 x+4 y-2 x+y \)

Let's analyze the expressions you've provided and simplify or solve them step by step. 1. **Expression 1:** \( x^{2}+7x+10 \) 2. **Expression 2:** \( x^{2}+7x-10 \) 3. **Expression 3:** \( x^{2}+5x+b \) 4. **Expression 4:** \( 3ab+6b-3a+2b \) 5. **Expression 5:** \( 2x+4y-2x+y \) ### Step 1: Simplifying Each Expression **Expression 1:** \( x^{2}+7x+10 \) This is a quadratic expression. We can factor it: \[ x^{2}+7x+10 = (x+2)(x+5) \] **Expression 2:** \( x^{2}+7x-10 \) This is also a quadratic expression. We can use the quadratic formula to find its roots: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \( a = 1, b = 7, c = -10 \). Calculating the discriminant: \[ b^2 - 4ac = 7^2 - 4 \cdot 1 \cdot (-10) = 49 + 40 = 89 \] Now applying the quadratic formula: \[ x = \frac{-7 \pm \sqrt{89}}{2} \] **Expression 3:** \( x^{2}+5x+b \) This is another quadratic expression. We can express it in standard form, but we need the value of \( b \) to proceed further. **Expression 4:** \( 3ab+6b-3a+2b \) We can combine like terms: \[ 3ab + (6b + 2b) - 3a = 3ab + 8b - 3a \] **Expression 5:** \( 2x+4y-2x+y \) We can simplify this by combining like terms: \[ (2x - 2x) + (4y + y) = 0 + 5y = 5y \] ### Summary of Results 1. **Expression 1:** \( (x+2)(x+5) \) 2. **Expression 2:** Roots are \( x = \frac{-7 \pm \sqrt{89}}{2} \) 3. **Expression 3:** Remains \( x^{2}+5x+b \) (needs \( b \) for further simplification) 4. **Expression 4:** \( 3ab + 8b - 3a \) 5. **Expression 5:** \( 5y \) If you need further calculations or specific values for \( b \) or any other expression, please provide that information!