Q. 287 - Intermediate Algebra

Question

Why does ${(a+b)}^2$ result in a trinomial, but$(a - b)(a + b)$ result in a binomial?

Step-by-Step Solution

Answer

${\left(a+b\right)}^2$ results in a trinomial because the middle term is double the product of the terms.

$\left(a-b\right)\left(a+b\right)$ results in a binomial because there is no middle term.

Step 1. Given information

${\left(a+b\right)}^2$ results in a trinomial, but $\left(a-b\right)\left(a+b\right)$ results in binomial

Step 2.

${\left(a+b\right)}^2$ results in a trinomial because when we perform the product the inner and outer terms with FOIL are the same.

But the middle term is double the product of the terms.

Step 3.

$\left(a-b\right)\left(a+b\right)$ results in a binomial because when we perform the product the inner and outer terms with FOIL are opposite and there is no middle term.