Algebraic Expression

s

Algebraic Expression Terms

Factors of a term

Like and Unlike Terms

Expression Types

Forming Expression

Exercise – 1

Topics

Exercise – 2

Terms are each separate values in an expression.

Terms 

–3

–8xy

4x2

–5x3z2

All given values can be terms of an algebraic expression.

Algebraic Expression Terms

Expressions

An expression is made up of terms separated by operations, like plus and minus signs. Consider three terms 2x, 7 and 5y2, then an expression can given by:

2x - 7 + 5y2

– 5y2 + 2x + 7

5y2 + 2x + 7

7 - 2x + 5y2

And many more …

A variable is a letter that represents a value that can change.

A constant is a value that does not change.

An algebraic expression contains variables and constants.

In an algebraic expression, the constant with variable is called coefficient.

Variable

Constant

Expression

Coefficient

Factors of a term

A term consists of constants and variables. Either way, we can say a term is a product of its factors. So broken down a term in simplest form is called the factors of a term.Consider an expression: 4x2 – 3xy

In expression 4x2 – 3xy there are two terms 4x2 and – 3xy

Factors of 3xy are –3, x and y.

Factors of 4x2 are 4, x and x.

Like and Unlike Terms

When terms have the same algebraic factors, they are like terms. It means the term containing same variables.When terms have different algebraic factors, they are unlike terms.

Consider an expression: 5x2y – 3xz + 5x2y – 4 + 9y

 Example

Like terms: 5x2y and 5x2y.

Unlike terms: –3xz, 9y and –4.

Rules to identify Like and Unlike terms

(2) The order in which the variables are multiplied

in the terms.

Ignore the numerical coefficients. Concentrate on the algebraic part of the terms.

Check the variables in the terms. They must be the same.Next, check the powers of each variable in the terms. They must be the same. Note that in deciding like terms, two things do not matter

(1) The numerical coefficients of the terms

POLYNOMIALS

Expression Types

MONOMIALS

BINOMIALS

TRINOMIALS

An expression with only one term is called a monomial.

2xy, – 5m2, 3abc, 4z3, 9, etc. are examples of monomials.

An expression with two terms is called a binomial.

(7xy – y2), (3mn + 5n), (4z3 + 9), etc. are examples of binomials.

An expression with three term is called a trinomial.

(2xy – 5z2 + 9), (3m + n – 7), etc. are examples of trinomials.

In general, an expression with one or more terms is called a polynomial.

Forming Expression

Real problems in science or in business occur in ordinary language.  To do such problems, we typically have to translate them into algebraic language.

To translate a word problem into algebraic expression, remember these common phrases:

Add Subtract Multiply Divide Equals

plusaddsummore thanin addition togreater thantotal and

differencesubtractless thantake away

productoftimestwice (×2)factor

divided byquotientsplitsharedistribute

is

A number increased by twelve x + 12

The sum of twice a number and six 2x + 6

Eighty less than a number x – 80

Five greater than three times a number 3x + 5

Three times the total of a number and five3(x + 5)

Five more than twice a number 2x + 5

Three times a number decreased by 11 3x - 11

Translate statement into algebraic expression Use variable as ‘x’

Exercise – 1

How many terms are in the following expressions:

4x − 3

2

2x2 − 3x + 5

3

x2 − x + 5y2 − y

4

5xy − 3zx + 5xy2

3

xy − 0

1

− 3x2y

−1, 3, x, x and y

Find the factors of the following expressions:

−9nm2

−1, 3, 3, n, m and m

8pqr

2, 2, 2, p, q and r

3pqr

Monomial

Identify as monomials, binomials and trinomials:

3x + y – 3

Trinomial

x2 – 3y

Binomial

z2 – 3

Binomial

z2 – 3 – 5x

Trinomial

zx2 – 3 + 3xz2 – 5x + x2y

Identify Like and Unlike terms in the following expression:

Like Terms:

Unlike Terms:

zx2 and x2y

– 3, – 5x and 3xz2

4x2 – 3y2 + 3xz – 5x + y

Like Terms:

Unlike Terms:

No like terms.

All are unlike terms.

4m2 – 3nm + 3mn – 2n2

Like Terms:

Unlike Terms:

– 3nm and 3mn

4m2 and – 2n2

4pq – 3qp + 3p2q – 2pq2

Like Terms:

Unlike Terms:

4pq and – 3qp

3p2q and – 2pq2

xy – (x + y)

Sum of numbers x and y subtracted from their product

Translate statement into algebraic expression

2x – 8

Eight less than twice a numbers x

10 – p/2

Half of a numbers p is subtracted from 10

2m – 1 = 17

One less than twice a number m is seventeen.

Exercise – 2