Question

express as a trinomial (3x+1)(x-4) no brackets

Answer 1

To express the product \((3x + 1)(x - 4)\) as a trinomial, we can use the distributive property (also known as the FOIL method for binomials):

1. Multiply the first terms: \(3x \cdot x = 3x^2\)
2. Multiply the outer terms: \(3x \cdot -4 = -12x\)
3. Multiply the inner terms: \(1 \cdot x = 1x\)
4. Multiply the last terms: \(1 \cdot -4 = -4\)

Now, combine these results:

\[
3x^2 - 12x + 1x - 4
\]

Combine the like terms \(-12x\) and \(1x\):

\[
3x^2 - 11x - 4
\]

Therefore, the expression \((3x + 1)(x - 4)\) can be expressed as the trinomial:

\[
\boxed{3x^2 - 11x - 4}
\]