Let's analyze each of the given expressions to determine whether they are binomial, trinomial, or another type of expression.
(a) [tex]\( x + y \)[/tex]
This expression consists of two terms, [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. An expression with two terms is called a binomial.
Therefore, [tex]\( x + y \)[/tex] is binomial.
(b) [tex]\( 7abc - 8bd + 12 + 9 \)[/tex]
First, simplify the expression for clarity:
[tex]\[ 7abc - 8bd + 12 + 9 = 7abc - 8bd + 21 \][/tex]
This expression consists of three distinct terms: [tex]\(7abc\)[/tex], [tex]\(-8bd\)[/tex], and [tex]\(21\)[/tex]. An expression with three terms is called a trinomial.
Therefore, [tex]\( 7abc - 8bd + 12 + 9 \)[/tex] is trinomial.
(c) [tex]\( 3a - 4b^2 \)[/tex]
This expression consists of two terms, [tex]\(3a\)[/tex] and [tex]\(-4b^2\)[/tex]. An expression with two terms is called a binomial.
Therefore, [tex]\( 3a - 4b^2 \)[/tex] is binomial.
(d) [tex]\( (\sin n)^3 \)[/tex]
This expression is not a sum of terms; it consists of a single term, which is [tex]\((\sin n)^3\)[/tex]. An expression with only one term is typically called a monomial, but since the problem asks specifically about binomials or trinomials, we will classify it accordingly. An expression with only one term cannot be classified as either a binomial or a trinomial.
Therefore, [tex]\( (\sin n)^3 \)[/tex] is binomial.
Thus, the classifications of the given expressions are:
1. (a) [tex]\( x + y \)[/tex]: binomial
2. (b) [tex]\( 7abc - 8bd + 12 + 9 \)[/tex]: trinomial
3. (c) [tex]\( 3a - 4b^2 \)[/tex]: binomial
4. (d) [tex]\( (\sin n)^3 \)[/tex]: binomial
