Question

Which of the following is a binomial?
\[
  \left( A \right)8 \times a + a \\
  \left( B \right)7{a^2} + 8b + 9c \\
  \left( C \right)3a \times 4b \times 2c \\
  \left( D \right)11{a^2} + 11{b^2} \\
\]

Answer 1

Hint:In this question, we use the concept of algebraic expressions. Monomial, binomial, trinomial are the types of algebraic Expressions. In monomials have only one term, binomials have only two terms and trinomials have only three terms.

Complete step-by-step answer:

We have to select the binomial in the following options so we take one by one option.
First option, \[8 \times a + a\]
Now, first we have to solve \[8 \times a + a\]
$
   \Rightarrow 8 \times a + a = 8a + a \\
   \Rightarrow 9a \\
 $
\[8 \times a + a\] is a monomial because it contains only terms.
Second option, \[7{a^2} + 8b + 9c\]
\[7{a^2} + 8b + 9c\] is a trinomial because it contains three terms.
Third option, \[3a \times 4b \times 2c\]
Now, first we have to solve \[3a \times 4b \times 2c\]
\[ \Rightarrow 3a \times 4b \times 2c = 24abc\]
\[24abc\] is a monomial because it contains only terms.
Fourth option, \[11{a^2} + 11{b^2}\]
\[11{a^2} + 11{b^2}\] is a binomial because it contains two terms.
So, the correct option is (D).

Note: Whenever we face such types of problems we use some important points. First we solve the following option one by one then we observe which option has only two terms (binomial). So, we can easily select the correct option.