Final answer:
To express (4/3)x + 1 and (1/5)x + 3/2 as a trinomial, multiply the two expressions using the distributive property to get (4/15)x² + (11/5)x + 3/2 in its simplest form.
Step-by-step explanation:
The question appears to contain a slight error. However, I assume the intent was to express the products (4/3)x + 1 and (1/5)x + 3/2 as a trinomial. To clarify, a trinomial is a polynomial with three terms.
To combine these two expressions, we need to multiply them, which requires using the distributive property (also known as the FOIL method for binomials):
- Multiply the first terms: (4/3)x * (1/5)x = (4/15)x²
- Multiply the outer terms: (4/3)x * 3/2 = 2x
- Multiply the inner terms: 1 * (1/5)x = (1/5)x
- Multiply the last terms: 1 * 3/2 = 3/2
When we combine like terms, we get:
(4/15)x² + (2 + 1/5)x + 3/2
This is the trinomial expression in its simplest form.
To simplify further:
- Combine the x terms: (2 + 1/5)x = (10/5 + 1/5)x = (11/5)x
- The final simplified trinomial is (4/15)x² + (11/5)x + 3/2.