Questions: Express as a trinomial. (2 x-5)(2 x-3)

Transcript text: Express as a trinomial. \[ (2 x-5)(2 x-3) \]

Solution

Solution Steps

To express the given expression as a trinomial, we need to expand the product of the two binomials using the distributive property (also known as the FOIL method for binomials). This involves multiplying each term in the first binomial by each term in the second binomial and then combining like terms.

Step 1: Expand the Expression

We start with the expression \( (2x - 5)(2x - 3) \). To expand this, we apply the distributive property:

\[ (2x - 5)(2x - 3) = 2x \cdot 2x + 2x \cdot (-3) - 5 \cdot 2x - 5 \cdot (-3) \]

Step 2: Perform the Multiplications

Calculating each term, we have:

\[ 2x \cdot 2x = 4x^2 \] \[ 2x \cdot (-3) = -6x \] \[ -5 \cdot 2x = -10x \] \[ -5 \cdot (-3) = 15 \]

Step 3: Combine Like Terms

Now, we combine the like terms:

\[ 4x^2 - 6x - 10x + 15 = 4x^2 - 16x + 15 \]