Expand the Expression: (2y-3)(y-4) Using Binomial Multiplication

To solve the algebraic expression $(2y-3)(y-4)$, we will apply 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.

• Step 1: Multiply the first terms: $2y \times y = 2y^2$.
• Step 2: Multiply the outer terms: $2y \times -4 = -8y$.
• Step 3: Multiply the inner terms: $-3 \times y = -3y$.
• Step 4: Multiply the last terms: $-3 \times -4 = 12$.

Next, we combine all these results: $2y^2 - 8y - 3y + 12$.

Then, we combine the like terms $-8y$ and $-3y$ to get $-11y$.

Therefore, the expanded expression is $2y^2 - 11y + 12$.

This matches choice (3): $2y^2 - 11y + 12$.

Thus, the solution to the problem is $2y^2 - 11y + 12$.