Algebraic Expressions

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 4x 2 –5x 3 z 2 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 5y 2, then an expression can given by: 2x y 2 – 5y 2 + 2x + 7 5y 2 + 2x x + 5y 2 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: 4x 2 – 3xy In expression 4x 2 – 3xy there are two terms 4x 2 and – 3xy Factors of 3xy are –3, x and y. Factors of 4x 2 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: 5x 2 y – 3xz + 5x 2 y – 4 + 9y Example Like terms: 5x 2 y and 5x 2 y. 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, – 5m 2, 3abc, 4z 3, 9, etc. are examples of monomials. An expression with two terms is called a binomial. (7xy – y 2 ), (3mn + 5n), (4z 3 + 9), etc. are examples of binomials. An expression with three term is called a trinomial. (2xy – 5z 2 + 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: AddSubtractMultiplyDivideEquals plus add sum more than in addition to greater than total and difference subtract less than take away product of times twice (×2) factor divided by quotient split share distribute 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 five 3(x + 5) Five more than twice a number 2x + 5 Three times a number decreased by 11 3x - 11 Translate statement into algebraic expression Translate statement into algebraic expression Use variable as ‘x’

Exercise – 1 How many terms are in the following expressions: 4x − x 2 − 3x x 2 − x + 5y 2 − y 4 4 5xy − 3zx + 5xy xy − − 3x 2 y −1, 3, x, x and y −1, 3, x, x and y Find the factors of the following expressions: −9nm 2 −1, 3, 3, n, m and m −1, 3, 3, n, m and m 8pqr 2, 2, 2, p, q and r 2, 2, 2, p, q and r 3pqr Monomial Monomial Identify as monomials, binomials and trinomials: 3x + y – 3 Trinomial Trinomial x 2 – 3y Binomial Binomial z 2 – 3 Binomial z 2 – 3 – 5x Trinomial Trinomial

zx 2 – 3 + 3xz 2 – 5x + x 2 y Identify Like and Unlike terms in the following expression: Like Terms: Unlike Terms: zx 2 and x 2 y – 3, – 5x and 3xz 2 4x 2 – 3y 2 + 3xz – 5x + y Like Terms: Unlike Terms: No like terms. All are unlike terms. 4m 2 – 3nm + 3mn – 2n 2 Like Terms: Unlike Terms: – 3nm and 3mn 4m 2 and – 2n 2 4pq – 3qp + 3p 2 q – 2pq 2 Like Terms: Unlike Terms: 4pq and – 3qp 3p 2 q and – 2pq 2 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