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Algebraic Expressions

Algebraic Expressions. Topics. Algebraic Expression Terms. Factors of a term. Like and Unlike Terms. Expression Types. Forming Expression. Exercise – 1. Exercise – 2. Algebraic Expression Terms. Expressions. A variable is a letter that represents a value that can change. Terms.

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Algebraic Expressions

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  1. Algebraic Expressions

  2. Topics Algebraic Expression Terms Factors of a term Like and Unlike Terms Expression Types Forming Expression Exercise – 1 Exercise – 2

  3. Algebraic Expression Terms Expressions A variable is a letter that represents a value that can change. Terms Variable 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: Terms are each separate values in an expression. Constant A constant is a value that does not change. –3 –8xy An algebraic expression contains variables and constants. Expression 2x - 7 + 5y2 4x2 – 5y2 + 2x + 7 –5x3z2 Coefficient In an algebraic expression, the constant with variable is called coefficient. 5y2 + 2x + 7 All given values can be terms of an algebraic expression. 7 - 2x + 5y2 And many more …

  4. 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 expression4x2 – 3xy there are two terms 4x2and – 3xy Factors of 4x2are 4, x and x. Factors of 3xy are –3, x and y.

  5. 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. Ignore the numerical coefficients. Concentrate on the algebraic part of the terms. Example 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 Consider an expression:5x2y – 3xz + 5x2y – 4 + 9y Like terms:5x2y and 5x2y. (1) The numerical coefficients of the terms Unlike terms: –3xz, 9y and –4. The order in which the variables are multiplied in the terms. Rules to identify Like and Unlike terms

  6. Expression Types MONOMIALS An expression with only one term is called a monomial. 2xy, – 5m2,3abc, 4z3, 9, etc. are examples of monomials. BINOMIALS An expression with two terms is called a binomial. (7xy– y2), (3mn+ 5n), (4z3 + 9),etc. are examples of binomials. TRINOMIALS An expression with three term is called a trinomial. (2xy – 5z2+ 9), (3m + n – 7),etc. are examples of trinomials. POLYNOMIALS In general, an expression with one or more terms is called a polynomial.

  7. Forming Expression Translate statement into algebraic 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. Use variable as ‘x’ x + 12 A number increased by twelve To translate a word problem into algebraic expression, remember these common phrases: 2x + 6 The sum of twice a number and six x – 80 Eighty less than a number Three times the total of a number and five 3(x + 5) Five greater than three times a number 3x + 5 Five more than twice a number 2x + 5 Three times a number decreased by 11 3x - 11

  8. Exercise – 1 Identify as monomials, binomials and trinomials: How many terms are in the following expressions: Find the factors of the following expressions: − 3x2y 3pqr 4x − 3 8pqr −9nm2 z2–3 – 5x x2− x + 5y2− y xy− 0 5xy − 3zx + 5xy2 z2–3 x2–3y 2x2− 3x + 5 3x + y – 3 Monomial −1, 3, x, x and y 2 Trinomial 2, 2, 2, p, q and r Binomial Binomial −1, 3, 3, n, m and m 3 1 3 4 Trinomial

  9. Exercise – 2 Identify Like and Unlike terms in the following expression: Translate statement into algebraic expression 4pq – 3qp + 3p2q – 2pq2 4m2 – 3nm + 3mn– 2n2 4x2– 3y2 + 3xz – 5x + y zx2– 3 + 3xz2– 5x + x2y Sum of numbers x and ysubtracted from their product Eight less than twice a numbers x Half of a numbers pis subtracted from 10 One less than twice a number mis seventeen. No like terms. zx2and x2y – 3nm and 3mn 4pq and – 3qp Like Terms: Like Terms: Like Terms: Like Terms: xy– (x + y) 2m – 1 = 17 10 – p/2 2x – 8 4m2and – 2n2 – 3, – 5x and3xz2 All are unlike terms. 3p2q and – 2pq2 Unlike Terms: Unlike Terms: Unlike Terms: Unlike Terms:

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