Multiply a Binomial by a Trinomial

Multiply a Binomial by a Trinomial

When you multiply a binomial by a trinomial, the key idea is to distribute each term of the binomial across all three terms of the trinomial. Since a binomial has two terms and a trinomial has three, you should expect six products before simplifying.

1) Distribute carefully

If the expression looks like ((a+b)(c+d+e)), multiply:

• (a) by each term in the trinomial
• (b) by each term in the trinomial

Write every product clearly so no term is missed.

2) Combine like terms

After expanding, look for terms with the same variable part and same powers. Add or subtract those coefficients. This step gives the simplified result.

3) Watch signs and exponents

Be especially careful with negative signs. A negative times a negative is positive, and powers stay attached to their variable part during multiplication.

4) Check your work

A good check is to count the products: there should be six before combining like terms. You can also multiply in a different order or rewrite the result to see whether the terms match.

Example pattern

((x+2)(x^2-3x+4)) becomes (x(x^2-3x+4)+2(x^2-3x+4)), then simplify.

Take your time, expand fully, and always finish by combining like terms.