Question

Writing Exercises

353. Why does (a + b)² result in a trinomial, but (a − b)(a + b) result in a binomial?

Answer 1

In
`$(a+b)^(2)$` is obtained by addition therefore result is trinomial while in (a-b)(a + b) the middle terms are canceled out of each other therefore result is binomial.

Explanation:

Explanation

• Given that
  `(a+ b)^(2)$` results in a trinomial, but (a-b)(a-b) results in a binomial.
• An expression
  `$(a+b)^(2)$` when multiply and simplify it is equal
  `a^(2)+a b+a b+b^(2)=a^(2)+2 a b+b^(2)$` therefore it is trinomial. Here middle term is obtained by addition. While an expression (a + b) (a-b) when multiply and simplify it is equal to
  `$a^(2)-a b+a b+b^(2)=a^(2)+b^(2)$`therefore it is binomial because the middle that is positive ab is canceled by negative ab.