Answer:

Types of algebraic expressions may further be distinguished in the following five categories.

They are: monomial, polynomial, binomial, trinomial, multinomial.

1. Monomial: An algebraic expression which consists of one non-zero term only is called a monomial.

Examples of monomials:

a is a monomial in one variable a.

10ab2 is a monomial in two variables a and b.

5m2n is a monomial in two variables m and n.

-7pq is a monomial in two variables p and q.

5b3c is a monomial in two variables b and c.

2b is a monomial in one variable b.

2ax/3y is a monomial in three variables a, x and y.

k2 is a monomial in one variable k.

2. Polynomial: An algebraic expression which consists of one, two or more terms is called a polynomial.

Examples of polynomials:

2a + 5b is a polynomial of two terms in two variables a and b.

3xy + 5x + 1 is a polynomial of three terms in two variables x and y.

3y4 + 2y3 + 7y2 - 9y + 3/5 is a polynomial of five terms in two variables x and y.

m + 5mn – 7m2n + nm2 + 9 is a polynomial of four terms in two variables m and n.

3 + 7x5 + 4x2 is a polynomial of three terms in one variable x.

3 + 5x2 - 4x2y + 5xy2 is a polynomial of three terms in two variables x and y.

x + 5yz – 7z + 11 is a polynomial of four terms in three variables x, y and z.

1 + 2p + 3p2 + 4p3 + 5p4 + 6p5 + 7p6 is a polynomial of seven terms in one variable p.

3. Binomial: An algebraic expression which consists of two non-zero terms is called a binomial.

Examples of binomials:

m + n is a binomial in two variables m and n.

a2 + 2b is a binomial in two variables a and b.

5x3 – 9y2 is a binomial in two variables x and y.

-11p – q2 is a binomial in two variables p and q.

b3/2 + c/3 is a binomial in two variables b and c.

5m2n2 + 1/7 is a binomial in two variables m and n.

4. Trinomial: An algebraic expression of three non-zero terms only is called a trinomial.

Examples of trinomial:

x + y + z is a trinomial in three variables x, y and z.

2a2 + 5a + 7 is a trinomial in one variables a.

xy + x + 2y2 is a trinomial in two variables x and y.

-7m5 + n3 – 3m2n2 is a trinomial in two variables m and n.

5abc – 7ab + 9ac is a trinomial in three variables a, b and c.

x2/3 + ay – 6bz is a trinomial in five variables a, b, x, y and z.

5. Multinomial: An algebraic expression of two terms or more than three terms is called a multinomial.

Note: binomial and trinomial are the trinomials.

Examples of multinomial:

p + q is a multinomial of two terms in two variables p and q.

a + b + c is a multinomial of three terms in three variables a, b and c.

a + b + c + d is a multinomial of four terms in four variables a, b, c and d.

x4 + 2x3 + 1/x + 1 is a multinomial of four terms in one variable x

a + ab + b2 + bc + cd is a multinomial of five terms in four variables a, b, c and d.

5x8 + 3x7 + 2x6 + 5x5 - 2x4 - x3 + 7x2 - x is a multinomial of eight terms in one variable x.

These are the types of algebraic expressions explained with various types of examples.

Step-by-step explanation:

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