Degree Of Polynomial Types Of Polynomials...Polynomials An algebraic expression that involves...
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Algebraic Expressions and Identities Algebraic Expressions It is an expression containing variables, numbers and operators. Terms It is a constant, a variable or variables multiplied by a constant. Degree Of Polynomial It is the greatest exponent in various terms of polynomial. Types Of Polynomials An expression with one term. For e.g., 21x 2 y, 17x, 9p etc. An expression with two unlike terms. For e.g., 3x 2 + 4x, 5x + 9y etc. An expression with three unlike terms. For e.g., 3x 2 + 5x - 9, a + b - c etc. Trinomial Binomial Monomial 1 2 3 Step 1 : Group all the like terms together in two polynomials. Step 2 : Combine all the like terms to get balance polynomial. Step 3 : Combine all the like terms to get balance polynomial. Step 1 : Change the sign of all terms of polynomial to be subtracted. Step 2 : Group all the like terms together. Coefficient When a constant is multiplied by a variable, the constant is called its coefficient. Degree The sum of a term’s exponent. Exponent of a constant is considered to be zero. Like Terms Terms in which same variable is raised to same exponent. Unlike Terms Terms which do not have same variable or exponent or both. Polynomials An algebraic expression that involves operations of addition, subtraction, multiplication and non-negative integer exponents of variable. A single variable polynomial of degree n is, a n x n + a n-1 x n-1 + ... + a 0 x 0 Addition and Subtraction Of Polynomials Addition 1 Subtraction 2 Algebraic Identity It is an equality that holds for any values of its variable. Important Algebraic Identities ( a + b ) 2 = a 2 + 2ab + b 2 1 ( a - b ) 2 = a 2 - 2ab + b 2 2 a 2 - b 2 = ( a + b )( a - b ) 3 a 2 + b 2 = ( a + b ) 2 - 2ab = ( a - b ) 2 + 2ab 4 ( a + b ) 3 = a 3 + b 3 + 3ab( a + b ) 5 ( a - b ) 3 = a 3 - b 3 - 3ab( a - b ) 6 a 3 + b 3 = ( a + b )( a 2 - ab + b 2 ) 7 a 3 - b 3 = ( a - b )( a 2 + ab + b 2 ) 8 ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2ab + 2bc + 2ac 9 a 3 + b 3 + c 3 - 3abc = ( a + b + c ) x ( a 2 + b 2 + c 2 - ab - bc - ca ) 10 a 4 + a 2 + 1 = ( a 2 + a + 1 )( a 2 - a + 1 ) 11 a 4 - b 4 = ( a 2 + b 2 )( a + b )( a - b ) 12 a 8 - b 8 = ( a 4 + b 4 )( a 2 + b 2 )( a + b )( a - b ) 13
Transcript of Degree Of Polynomial Types Of Polynomials...Polynomials An algebraic expression that involves...
Algebraic Expressions and IdentitiesAlgebraic Expressions
It is an expression containing variables, numbers and operators.
TermsIt is a constant, a variable or variables multiplied by a constant.
Degree Of PolynomialIt is the greatest exponent in various terms of polynomial.
Types Of PolynomialsAn expression with one term. For e.g., 21x2y, 17x, 9p etc.
An expression with two unlike terms. For e.g., 3x2 + 4x, 5x + 9y etc.
An expression with three unlike terms. For e.g., 3x2 + 5x - 9, a + b - c etc. Trinomial
Binomial
Monomial1
2
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Step 1 : Group all the like terms together in two polynomials.
Step 2 : Combine all the like terms to get balance polynomial.
Step 3 : Combine all the like terms to get balance polynomial.
Step 1 : Change the sign of all terms of polynomial to be subtracted.
Step 2 : Group all the like terms together.
CoefficientWhen a constant is multiplied by a variable, the constant is called its coe�cient.
DegreeThe sum of a term’s exponent. Exponent of a constant is considered to be zero.
Like TermsTerms in which same variable is raised to same exponent.
Unlike TermsTerms which do not have same variable or exponent or both.
PolynomialsAn algebraic expression that involves operations of addition, subtraction,multiplication and non-negative integer exponents of variable.A single variable polynomial of degree n is, anxn+ an-1xn-1+ ... + a0x0
Addition and Subtraction Of PolynomialsAddition1
Subtraction2
Algebraic IdentityIt is an equality that holds for any values of its variable.
Important Algebraic Identities( a + b )2 = a2 + 2ab + b2 1
( a - b )2 = a2 - 2ab + b2 2
a2 - b2 = ( a + b )( a - b )3
a2 + b2 = ( a + b )2 - 2ab = ( a - b )2 + 2ab
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( a + b )3 = a3 + b3 + 3ab( a + b ) 5
( a - b )3 = a3 - b3 - 3ab( a - b ) 6
a3+ b3 = ( a + b )( a2 - ab + b2 ) 7
a3- b3 = ( a - b )( a2 + ab + b2 ) 8
( a + b + c )2 = a2+ b2+ c 2 + 2ab + 2bc + 2ac 9
a3+ b3+ c3 - 3abc = ( a + b + c ) x ( a2+ b2+ c 2- ab - bc - ca )
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a4+ a2+ 1 = ( a2+ a + 1 )( a2- a + 1 )11
a4 - b4 = ( a2 + b2 )( a + b )( a - b )12
a8 - b8 = ( a4 + b4 )( a2 + b2 )( a + b )( a - b )13
