Question

1. express as a trinomial: (2x - 5)(x + 3) 8. express as a trinomial: (2x - 3)(2x - 1)

Explanation:

Step1: Apply FOIL to first expression

$$\begin{align*} (2x - 5)(x + 3) &= 2x \cdot x + 2x \cdot 3 - 5 \cdot x - 5 \cdot 3 \\ &= 2x^2 + 6x - 5x - 15 \end{align*}$$

Step2: Combine like terms (first expression)

$2x^2 + (6x - 5x) - 15 = 2x^2 + x - 15$

Step3: Apply FOIL to second expression

$$\begin{align*} (2x - 3)(2x - 1) &= 2x \cdot 2x + 2x \cdot (-1) - 3 \cdot 2x - 3 \cdot (-1) \\ &= 4x^2 - 2x - 6x + 3 \end{align*}$$

Step4: Combine like terms (second expression)

$4x^2 + (-2x - 6x) + 3 = 4x^2 - 8x + 3$

Answer:

1. $2x^2 + x - 15$
2. $4x^2 - 8x + 3$