Algebra PPT
- 1. ALGEBRA
- 2. INTRODUCTION Algebraic expression – a group of numbers, symbols, and variables that express an operation or a series of operations. EXAMPLES: a-8 b-2 z+12 etc……
- 3. DEFINITIONS Variable – A variable is a letter or symbol that represents a number. It is an unknown quantity EXAMPLES: 5+z=13 4-y=1 etc……
- 4. Evaluating an algebraic expression – To find the value of an algebraic expression we can substitute numbers for variables. Examples: m+7,m-3 etc… (‘m’ variable can be any number) m + 8 if m = 2 then 2 + 8 = 10 z – 6 if z = 10 then 10 - 6 = 4
- 5. Like and unlike terms Like terms: like terms are terms that have the same variables and powers Example: 8xyz2 and 5xyz2 are like terms because they have the same variables and power
- 6. unlike terms: Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. Example: 3abc and 3ghi are unlike terms because they have different variables
- 7. Difference between like and unlike terms 1.Like terms can be added together to simplify an expression. 2.When adding like terms, add the numerical coefficients and retain the variable. 3.Unlike terms cannot be added together since the variables represent different items.
- 8. Words That Lead to Addition Sum More than Increased Plus Altogether
- 9. Words That Lead to Subtraction Decreased Less Difference Minus How many more
- 10. Terms and coefficients Terms: Terms are the elements separated by the plus or minus signs. Example: 3x2+2y+7xy+5 This example has four terms, 3x2, 2y, 7xy, and 5.
- 11. Coefficients: A number used to multiply a variable. Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient.
- 12. Monomials,binomials,trinomials and polynomials Monomial: An expression with one term is called a monomial Binomial: An expression with two terms is called a binomial
- 13. Trinomial: An expression with three terms is called a trinomial Polynomial: A polynomial is an expression consisting of variables and coefficients more than three terms.
- 14. Examples: ,
- 15. Identity 1. An identity is an equality, which is true for all values of the variables in the equality 2. An equation is not an identity.
- 16. Standard identities 1) (a+b)2 = a2 + 2ab + b2 2) (a-b)2 = a2-2ab + b2 3) (a+b) (a-b) = a2-b2 4) (x+a)(x+b)=x2 +(a+b)x+ab
- 17. Ten more than a number n+10 A number decrease by 5 w-5 6 less than a number z-6 A number increased by 8 n+8 The sum of a number & 9 n+9 4 more than a number y+4
- 18. A number s plus 2 s+2 A number decrease by 1 k-1 31 less than a number x-31 A number b increased by 7 b=7 The sum of a number & 6 n=6 9 more than a number z=9