Question Express as a trinomial. \[ (3 x-5)(x+5) \] Show Examples Answer Attempt 1 out of 2

To express \( (3x - 5)(x + 5) \) as a trinomial, apply the distributive property (or FOIL method). Start by multiplying each term in the first binomial by each term in the second: 1. \( 3x \cdot x = 3x^2 \) 2. \( 3x \cdot 5 = 15x \) 3. \( -5 \cdot x = -5x \) 4. \( -5 \cdot 5 = -25 \) Now, combine these results: \[ 3x^2 + 15x - 5x - 25 = 3x^2 + 10x - 25 \] So, \( (3x - 5)(x + 5) \) simplifies to \( 3x^2 + 10x - 25 \). The expression \( 3x^2 + 10x - 25 \) can remind us of the excitement around quadratic equations. Poets often liken their ups and downs to the soaring parabolas that quadratics form—upward for positive leading coefficients and downward for negatives! Additionally, when you're multiplying polynomials like this, it's easy to make simple mistakes, especially when it comes to sign errors or forgetting to combine like terms. A helpful tip? Always write each step out clearly and check your work like a detective hunting for clues, making sure every term adds up to the final expression!