Question Express as a trinomial, \[ (3 x+4)(2 x+4) \] Answer Attempt 1 out of 2

To express \( (3x + 4)(2x + 4) \) as a trinomial, we can use the distributive property (also known as the FOIL method for binomials). Multiplying the first terms gives \( 3x \cdot 2x = 6x^2 \). Next, multiply the outer terms: \( 3x \cdot 4 = 12x \). Now for the inner terms, we have \( 4 \cdot 2x = 8x \). Lastly, multiply the last terms: \( 4 \cdot 4 = 16 \). Now, sum these results: \[ 6x^2 + 12x + 8x + 16 = 6x^2 + 20x + 16. \] So, the trinomial is \( 6x^2 + 20x + 16 \). Did you know that polynomials, including trinomials, have been used for centuries? The origins of algebra date back to ancient civilizations like Babylon and Egypt, where people first started solving problems with unknowns. In terms of real-world applications, trinomials often pop up in areas like physics, particularly in motion equations, or in finance when calculating the profit or losses in investment scenarios. This makes understanding them quite beneficial beyond the classroom!