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Algebraic Expressions and Identities by Siby Sebastian PGT(Maths)

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## Algebraic Expressions and Identities by Siby Sebastian PGT(Maths)

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**Algebraic Expressions and IdentitiesbySiby Sebastian**PGT(Maths)**Mathematical Expressions**We are familiar with the following type of numerical expressions: 12 + 6 3 x 12 6 (3 + 2) 15 - 4 (6)**What is a variable?**Consider the expressions x + 12 3y – 2**What is a variable?**x + 12 , 3y – 2 These expressions involve certain letters x and y . Any value can be assigned to these letters. A variable is a letter or symbol that represents an unknown value.**Algebraic Expressions**When variables are used with other numbers, parentheses, or operations, they create an algebraic expression. x + 2 (a) (b) 3m + 6n - 6**What is a term?**A term is the name given to a number, a variable, or a number and a variable combined by multiplication or division separated by the operation of addition or multiplication.**TERMS**AlgebraicExpression a + 2 Terms a , 2 Algebraic Expression 3m + 6n - 6 Terms 3m, 6n, - 6**What are coefficients?**A coefficient is the numerical factor of the term of an algebraic expression. Algebraic Expression Term Coefficient 6m + 5 6m 6 8r + 7m + 4 7m 7 14b - 8 14b 14**What are constants?**A constant is a number in an expression that cannot change its value. In the expression: 5x + 7y - 2 the constant is - 2. Find the constant in 10ab - 4b+17a - 50 ?**Figure it out!**Identify the terms, coefficients, and constants. 1. 12a - 6b + 4 2. 4x - 2y 3. c - 32 4. 3x + 2**Write algebraic expressions for these word phrases**• Four more than s • The product of 7 and c • Nine less than x • A number divided by the sum of 4 and 7. • Twice the sum of a number plus 4. • The sum of ¾ of a number and 7. • Ten times a number increased by 150.**MONOMIALS**2x 3ab 4y2 These expressions have only one term. Such expressions are called MONOMIALS**BNOMIALS**2x -3y 3ab + 8b2 4y2 + 16z These are expressions having two terms. Such expressions are called BINOMIALS**TRINOMIALS**2x -3y -10 3ab + 8b2 + 20 4y2 + 16z -5 These are expressions having three terms. Such expressions are called TRINOMIALS**POLYNOMIALS**Algebraic Expressions having one or more terms with non zero coefficients and non negative integral powers for the variable are called POLYNOMIALS 2x , 3x+15 , 2x-3y+2, 3xy – 4y + 2x3 +7y2 -10, 2x5 +4xy3 +10xy-3, 2ab + 4a2 – 6b2 - 2a - 3b + 2**LIKE TERMS**Like terms are terms having same variables with same powers. But their coefficients may be different. Examples 1. 2xy , -5xy, 10xy, 2. 2a2b , -10 a2b, a2b**IDENTIFY LIKE TERMS**3x3yz , 4x, -5y , x3 , 5xy, -5xyx3, 2y , -7xyz, 10x, 27xy, 22y , 6yz**OPERATIONS ON POLYNOMIALS**POLYNOMIALS CAN BE 1.ADDED 2.SUBTRACTED 3.MULTIPLIED AND 4.DIVIDED**QUIZ**• In the expression 3x+y2 name the terms. 2. What is the coefficient of -3xy? • Are 2xy and 2x2y like terms? • Are 3x2y and -2yx2 like terms?**QUIZ**5. What is the maximum and minimum number of terms in a polynomial? 6. Is 5 an algebraic expression? 7. What are the variables in the equation 7x2y + 8xy2 ? Are they like terms?